This answer assumes that the claim is about whether you shall put creams and oitments as a first aid in minor burns.
First aid is what you do before/until an ambulance arrives with a paramedic.
Applying creams to minor burns as a first aid:
Based on claims from authoritative medical websites, it is not recommended nor appropriate to apply any types of creams on burns.
National Health Service (NHS), which is the largest and the oldest single-payer healthcare system in the world, mentioned on their website reported in a post:
Cool the burn with cool or lukewarm water for 10 to 30 minutes, ideally within 20 minutes of the injury occurring. Never use ice, iced water or any creams or greasy substances such as butter.
MedlinePlus, which is a National Institutes of Health website, warned in a post to:
not use cream, lotion, oil, cortisone, butter, or egg white.
Many sites advised to put hydrocortisone cream on burn like mayoclinic.org:
Apply moisturizer, aloe vera lotion or gel, or low-dose hydrocortisone cream, which may provide relief in some cases. (unreferenced)
But, it has been warned not to use on burns by Truven Health Micromedex, the official producer of the drug, information delivered by website drugs.com:
This medicine is for use on the skin only. Do not get it in your eyes, nose, mouth, or vagina. Do not use it on skin areas that have cuts, scrapes, or burns. If it does get on these areas, rinse it off right away with water.
Soak the burn in cool water. Then treat it with a skin care product like aloe vera cream.
The problem with this claim is that aloe vera is a gel not a cream, there is a slight difference, aloe vera gel has been proven to be effective for burns.
Applying ointments to minor burns as a first aid:
Based on claims from authoritative medical websites, it is not recommended nor appropriate to apply ointments on burns.
http://www.stjohn.org.nz/ reported that:
DO NOT apply creams, ointments, lotions or butter to any burn injury because infection may occur and complicate the injury.
The American Academy of Pediatrics, an organization of 57,000 primary care pediatricians, pediatric medical subspecialists, and pediatric surgical specialists dedicated to the health, safety, and well-being of infants, children, adolescents, and young adults, said in a report:
Do not break any blisters. This could allow bacteria into the wound. Never put grease (including butter or medical ointments) on the burn. Grease holds in heat, which may make the burn worse. It also makes the burn harder to examine by medical personnel later.
Since all claims so far seem authoritative, here is some evidence which show that creams or ointments are not appropriate as a first aid:
In a very notable study by US National Library of Medicine National Institutes of Health, it is reported in PRE-HOSPITAL CARE paragraph, THERMAL BURNS sub-paragraph, that you shall not put any types of ointments or creams, section 10:
The study added also:
Moreover, removal of such substances might also be difficult and painful to the patient.
Another study, a review of first aid treatments for burn injuries, was hidden behind a paywall, now it is on my google drive reviewed:
common first aid and pre-hospital treatments for burns (water—cold or warm, ice, oils, powders and natural plant therapies), possible mechanisms whereby they might work and the literature which supports their use.
The study mentioned:
At the time of the earliest first aid recommendations (1880)
[3,39,67], it was suggested that burnt surfaces should be
protected from air, and anointed well with oil (lamp oil, salad
oil, castor oil or carron oil from a chemist) or painted over with
grease or butter, with carbolic acid or thymol added to the oily
cotton wool dressing. The use of oil was probably based on the
common perception at the time that immediate treatment of
burns was needed to prevent exposure to the air, not only to
alleviate pain , but also to prevent further damage as
described by Martin in 1886 : ‘‘Fatal damage may be done in
a few moments by exposing a badly burnt chest, or abdomen,
to the air before anything is ready to cover it with.’’. Oils and
fats on the skin form a very effective air barrier.
By 1901, the recommendations for first aid treatment of
burns/scalds were clearly segregated depending on wound
depth , with treatment of flour, whiting or powdered chalk
recommended for burns where the skin was ‘‘merely reddened’’,
compared to covering with oils (carron, olive, salad,
linseed, almond or cod-liver), Vaseline1, lanoline or cold cream
when the skin was blistered or charred. Around the 1940s belief
had changed that local application of oils and ointments to the
skin was not beneficial and made secondary treatment by the
doctor/surgeon more difficult . Instead, first aiders were
instructed to cover the burnwith a clean or sterile cloth and send
the patient to hospital or a first aid post (military).
You can read the full study and find appropriate references there.
Conclusion: You shall never use creams or ointments as a first aid for any burn.