This really reads like you are assuming that x == [no dog will choose to starve to death in the presence of food] is true and then the rest of the argument simply follows from x.
Are you asking for any particular type of formal proof of the negative?
Or would the fact that there are no known cases of this phenomenon recorded in the recorded history of dogs, even in places dogs have been revered, be adequate?
In my view, if you're looking for formal proof of a negative, you've already insisted on an impossibility, so there's no hope of persuading you anyway.
I did not ask for a formal proof, but a stronger proof than you not having heard of such a thing happening. It is just about plausible to me that a dog can refuse to eat and starve; dogs do get very depressed.
Anyway, by this method of denying the possibility of animals acting in a certain way until a counterexample is presented, you can ascribe any number of unique traits to humans; but they all stem from your default assumption that humans are unique. It's not particularly interesting to merely restate an assumption.
Is there any evidence for x?