If I would let him, one of my dogs would happily live off of the cat's litter box.

I do have one dog who has allergies (it is the rescue mix -both of the pure bred are super healthy about what they can eat-one I got from a breeder and the pup is a breeder turn in to rescue because he is not show quality) and the wrong food will send him into skin itch/open sore hell. Interestingly enough - he cannot handle some of the really expensive kibble either - it will create the problem just as much as some of the cheaper brands. I have found two brands he can eat without incident - so that is what all of them eat. For awhile I thought I was going to have to make all their dog food by grinding chicken or lamb and adding in vegetables and so forth. And while I found it fun to experiment with for awhile, it got exhausting and I was greatly relieved when I found the two commercial brands that worked.

On the vet thing - I have gone to vets who pushed the brands they were selling in their offices even where my dogs were fine on grocery store dog food and I have seen those who only used specialty food to treat a specific situation and only until it cleared up.
I had a cat once who cost me a fortune in special canned food for a chronic problem.