The sentence is technically true, albeit drawing any conclusion about animal feelings from it would be very questionable.
Our neurons secrete several substances, such as neurotransmitters, neuromodulators and neurohormones in many different situations. The same molecules are used by a dog's neurons, or by those of a fruit fly or an earthworm for that matters.
The fact that the roundworm C. elegans is one commonly used animal model in neuroscience (although probably not as common as mice and rats) should be proof of that.
One should understand the same molecule can be secreted in completely different situations, they are not specific for a certain emotion. The sentence you quote is meaningless in that there is no specific "love substance" secreted by the brain.
From the abstract of: The Neurobiology of Love - Esch and Stefano 2005
Love is a complex neurobiological phenomenon, relying on trust, belief, pleasure and reward activities within the brain, i.e., limbic processes. These processes critically involve oxytocin, vasopressin, dopamine, and serotonergic signaling. Moreover, endorphin and endogenous morphinergic mechanisms, coupled to nitric oxide autoregulatory pathways, play a role.
Note that all those molecules are also secreted in completely different situations.
Dopamine is also important for drug addiction, processing of food rewards, or gambling.
Vasopressin is important for many things, including regulating water excretion by the kidney.
Oxytocin has mostly been described for its effect during parturition and lactation, namely stimulating uterine contraction (it is a drug commonly used when labour needs to be induced), and for the milk let-down reflex.
However, it is also implicated in a variety of other situations such as regulation of bone metabolism and adipogenesis, obsessive-compulsive disorder, regulation of cardiac contraction and many more.
Similar things can be said for serotonin, and endogenous opioids but really the point is not to list every possible action of every neurotransmitter in the brain (there are plenty of 1000+ pages books that do that...) but rather to understand that different neurotransmitters, released at different sites, at different concentrations, in different patterns, in different combinations and different physio-pathological situations have different effects. No need to have one neurotransmitter for each single action the brain needs to perform, when information can be coded (and is coded) by modulating the way these molecules are secreted.
So, in summary, one may as well say:
When a dog sees its owner, its brain secretes the same substances as those secreted by an addict's brain when on a cocaine trip.
Which sounds less cute, I guess.