BBQ here means hot dogs and hamburgers, unless the host specifies- fancier BBQ would have steak, chicken breast, meat kebabs or sausage. I think the confusion comes from what the South calls BBQ- which is rarely done at home in Canada- with what we do more of, which is more what I believe is called "grilling" there.
However, that is completely beyond the point here- because the Mom was told the menu. I don't think it's fair to pick on the kids for not caring for the food- though they should not have (depending somewhat on age) made such a fuss about it. There's a whole thread about picky eating adults- and kids can be far more cautious about what they will and won't eat- even if they eventually grow out of it. My 4 year old won't touch leafy salad- and given his father can't eat it without stomach pain (crohn's disease), I'm not forcing him either. I wouldn't let him "gag" about food though- he knows even at 4 that he is to "eat around" things he doesn't like.
I lay the blame on the parents for either not admitting to their kids pickiness, or apologizing for their behaviour and correcting it if they aren't normally fussy- and also for complaining at the OP's menu instead of speaking up when they could have.