Vets don't know everything about nutrition. Some know very little at all. They recommend things like Science Diet, Eukanuba which is junk. HOWEVER, a month or two of a junky food is not going to hurt your pup when you are dealing with other issues.
Loki had giardia when he was a puppy and was on meds for that, and I made the mistake of also changing his food because I didn't like the junk the breeder had him on. That upset his stomach, so I tried an even better food. Finally my vet said STOP and leave him on whatever he's on for a month or two until he doesn't have any issues (We were also training, and I had to use kibble for treats.) She was right and eventually the issues all cleared up and I was able to switch his food (gradually, over 2 weeks) without any issues once he was around 10-12 months old.
Just stop changing things and let the little guy adjust
Bellasmom - Sam is like that too, but I don't know if it's because we got her when she was 10 months old? Or if she just always had an iron stomach? Either way it's generally a puppy thing and you can definitely indulge them a little bit more when they are older. I can even give my two a lick of ice cream or french fry and they are OK, but I could not do that when Loki was a puppy.