In another short: be careful with an unconditional "yes".
There are differences in honeys and conditions.
Honey can be a very effective treatment for a number of superficial wounds. And that is not only reported in recent medical publications but also ancient – wisdom.
But not all honeys are created equal.
Your first link goes to a site from New Zealand. The Manuka Honey originating there is known to have additional properties to the osmotic pressure, enzymes, phyto- and bee-chemicals etc.
But it is also important to qualify the actual 'ordinary' honey used. Some honeys might come from areas, plants, bees that are highly polluted, infected or simply full of toxins.
Conclusion: some honeys will prove an excellent treatment for a range of symptoms, diseases and wounds. But probably not for all types of wounds. Some honeys might make things worse.
BA Minden-Birkenmaier & GL Bowlin: "Honey-Based Templates in Wound Healing and Tissue Engineering", Bioengineering (Basel). 2018 Jun 14;5(2). pii: E46. doi: 10.3390/bioengineering5020046.
Over the past few decades, there has been a resurgence in the clinical use of honey as a topical wound treatment. A plethora of in vitro and in vivo evidence supports this resurgence, demonstrating that honey debrides wounds, kills bacteria, penetrates biofilm, lowers wound pH, reduces chronic inflammation, and promotes fibroblast infiltration, among other beneficial qualities.
Sami K. Saikaly & Amor Khachemoune: "Honey and Wound Healing: An Update", Am J Clin Dermatol (2017) 18:237–251 DOI 10.1007/s40257-016-0247-8
- Honey exerts its effects on wound healing through its antimicrobial properties and the alteration of physiologic and immunologic functions.
- The successful use of honey has been reported for a multitude of wounds, including burns, surgical sites, infected surgical wounds, chronic ulcers, malignant wounds, and neonatal wounds, among others.
- Systematic reviews have found ‘‘high quality evidence’’ and ‘‘unequivocal results’’ that honey is a superior dressing (relative to conventional dressings) and helps accelerate healing when treating partial thickness burns.
K Niaz et al.: "Health Benefits of Manuka Honey as an Essential Constituent for Tissue Regeneration", Curr Drug Metab. 2017;18(10):881-892. doi: 10.2174/1389200218666170911152240.
Honey is known for its therapeutic properties from ancient civilizations. Recently, the mechanism of action of Manuka honey in wound healing, epithelial regeneration, and ulcer treatments has been revealed.
In the current review, the health perspectives of honey, its chemical composition with special reference to flavonoids, polyphenol, and other bioactive trace compounds used in tissue regeneration have been discussed in detail.
We undertook a structured search using wide spectrum sources like Google Scholar, PubMed, and Scopus.
The included papers showed that Manuka honey can inhibit the process of carcinogenesis by controlling different molecular processes, and progression of cancer cells. Manuka honey has been found to have various biological activities, including antioxidant, antimicrobial and anti-proliferative capacities. Scientists try to use Manuka honey in the area of tissue engineering to design a template for regeneration. Naturally derived antibacterial agents of Manuka honey are numerous mixtures of different compounds, which can influence antibacterial capacity. The non-peroxide bacteriostatic properties of Manuka honey are associated with the presence of methylglyoxal (MGO).
In addition to bacterial growth inhibition, glyoxal (GO) and MGO from Manuka honey can enhance wound healing and tissue regeneration by their immunomodulatory property. Further studies are needed to provide detailed information about active components of Manuka honey and their potential efficacy in different diseases.
I Negut: "Treatment Strategies for Infected Wounds", Molecules. 2018 Sep 18;23(9). pii: E2392. doi: 10.3390/molecules23092392.
From the abstract:
A promising, but still an underrated group of potential antibacterial agents that can be integrated into wound dressings are natural products, especially essential oils. Some of the most commonly used essential oils against multidrug-resistant microorganisms, such as tea tree, St. John’s Wort, lavender and oregano, together with their incorporation into wound dressings are presented. In addition, another natural product that exhibits encouraging antibacterial activity is honey. We highlight recent results of several studies carried out by researchers from different regions of the world on wound dressings impregnated with honey, with a special emphasis on Manuka honey.
Honey has been used for decades as a natural healing agent for many human diseases for instance cardiovascular and gastrointestinal tract ailments, and infections of upper respiratory tract, as well as in infected wounds . The therapeutic properties of honey such as the capability to provide a topical nutrition to the wound, inflammation reduction, granulation and angiogenesis stimulation, wound epithelialization, recommend it to be integrated into wound dressings . The research carried out during last decades demonstrated that honey’s bacteriostatic and bactericidal activity can be ascribed to several factors:
- It’s acidic pH (regularly in the range of 3.4–6.1). It has been found that the acidic character of honey may encourage macrophages to eradicate bacteria and inhibit microbial biofilm establishment .
- The osmotic pressure applied by sugars found in its chemical composition. The high osmolality obstructs microbial development .
- The presence of antibacterial components such as hydrogen peroxide, antioxidants, lysozyme, phenolic acids, flavonoids, methylglyoxal and bee peptides (such as defensin-1) [130,131]. The production of hydrogen peroxide is a crucial component for the inhibition of bacterial development. In particular, hydrogen peroxide is gradually released/formed when the wound exudate interrelates with glucose oxidation, triggering the oxidative damage to pathogens’ macromolecules; hydrogen peroxide can react with the bacterial cell wall, as well as with intracellular lipids, proteins and nucleic acids
Taking into account the abovementioned, studies on different honey types revealed their high efficiency against the most prevalent microorganisms that are involved in wound infections. The investigations published by Kus ́ and coworkers  have shown that from 14 honey varieties from Poland analyzed for their antimicrobial activity, cornflower, buckwheat and thyme honeys were the most active against the growth of S. aureus PCM 2051 strain at concentrations of 3.12 or 6.25% (v/v). In the same study, adequate action was observed for linden tree, heather, savory and coriander honeys. Likewise, growth inhibition of a broad range of MRSA microorganisms has been reported by using of Ulmo tree , melaleuca  and longan flower  honeys, from many geographical regions.
However, in the presence of catalase- an enzyme that reduces the hydrogen peroxide- honey displays a diminished antimicrobial action. Moreover, the composition of honey is dependent on the floral source, bee species and geographical setting . To surpass this limitation, and problems generated by “traditional honeys” (such as the presence of spores that results in deactivation of glucose oxidase) only honeys with certified activities are recommended to be applied in medical domains. Therein, an assortment of medical honeys have entered the market (for example chestnut, manuka, thyme, revamil)  which exhibit, by comparison with “traditional honeys” good predictability and quality. At present, some companies are focused on producing dressings containing honey (mostly Manuka honey): Actilite®, Algivon®, MediHoney®, and Activon Tulle® .
Manuka honey, which is obtained from the Manuka tree and comprises a non-peroxide, non-degradable by the action of catalase component, can sustain its antibacterial activity in biological fluids . The antibacterial properties exerted by Manuka honey are not only attributed to the hydrogen peroxide but also to the high amounts of the antibacterial compound, methylglyoxal, present in its chemical composition . It was found that Manuka honey impedes the growth of MRSA and S. pyogenes, along with tested gram-negative strains (such as E. coli, and P. aeruginosa)  and eludes biofilm establishment on the wound site . Considering the beneficial multifaceted properties of this specific type of honey, in terms of the anti-inflammatory activity, wound repair efficacy and antibacterial properties, many research groups fabricated Manuka honey dressings. Minden-Birkenmaier et al. focused their study on fabrication and characterization of Manuka honey-containing poly(e-caprolactone) (PCL) nanofiber scaffolds to be applied as wound dressings and precursors to tissue-engineered skin. The obtained results confirmed that honey positively influenced in vitro fibroblasts infiltration into the scaffold, while inhibiting the growth of E. coli strain . Moreover, Yang and coworkers, incorporated Manuka honey as a functional antibacterial agent in an electrospun membrane produced with silk fibroin. The obtained fibrous matrices exhibited antibacterial activity against MRSA and methicillin-susceptible S. aureus, E. coli and P. aeruginosa . In a study by Tavakoli et al., a highly concentrated honey-Poly(vinyl alcohol) hybrid hydrogel was produced not only to promote antibacterial activity, but also to prove its biocompatibility. It was observed that the honey/Poly (vinyl alcohol) hybrid effectively encouraged the wound healing process by establishing a thin layer of hydrophilic gel that reduces the risk of contamination. Same dressing proved to be effective against S. aureus and E. coli pathogens .
As regarding the clinical benefits of honey, a recent review outlines observation reports and randomized controlled trials, as well as an update of the recently published literature . However, literature reports varied honey’s outcomes depending on the wound type and also it has been shown that honey may even have harmful effects. These incongruous results point toward that more information is needed and large randomized clinical trials are essential to demonstrate the clinical benefit of honey in reducing the prevalence of wound infections.