I would not have put up with it. This is a HUGE peeve of mine. At first I would have been nice, but by the 3rd or fourth meal and or whining session I would have told the person off.
Eat or don't eat what ever you want, but don't make it someone else's issue and don't ever, ever, ever say "no" to an idea unless you have a counter idea ready. If someone says "Chez Meathouse" and you open your guide book and say "oh, actually how about Hummus Chateau 3 blocks way", that's cool, but if someone says "Chez Meathouse" and you whine and say "but I can't eeeeeeeeeeeeeeeeeeeeat there!" you can just just sit outside and pout by yourself while the rest of us get our carnivore on. Bonus if its raining and we get a window table.
Guide books, for tourists and most likely for locals as well, are not hard to come by and list restaurants by all sorts of methods - by food, by neighborhood, by price. Picky eaters especially should invest in one or more.
In a group, everyone has to compromise a little, and sometimes in a restaurant of "familiar" foods is super fun (McDonalds in Japan has rice balls, in London people eat Pizza Hut with utensils, etc) to see how is done there, but food exploration is a HUGE HUGE HUGE part of traveling and under no circumstances would I let someone's pickiness stifle my foodie-ness continuously. People can make do, or separate but dictating and whining are not ok.