Sounds like me and my mother.... Funny though, the only boughten hamburger I can eat without those consequences is McDonald's plain little hamburger or Whataburger's junior burger.
Could it be something like irritable bowel syndrome or colitis caused by preservatives or some other additives in restaurant food? If he can eat at home and not have that problem, then there is something in restaurant food that is not in home cooked food, and I would try to narrow that down. I gave up on trying to figure it out, myself, and just have accepted that I can't eat certain foods (Long John Silver is the worst, also Olive Garden, any other hamburgers or chicken nuggets or chicken sandwiches, taco bell, nice restaurants, Asian food, you name it if it is from a restaurant.) I can make the equivalents at home and not have the problem, and my mom too. I just avoid eating out most of the time.
I don't know what would be in restaurant food that isn't in home cooked food except for preservatives, maybe liquids added to meats to plump them up, flavorings, ????
I hope he's able to identify what the problem is.