Yeah, there's something to be said from a Miss Manners POV that if you accept an invite to a private function where you know there will be prayers, then bowing your head on request (or if you know it's expected) is showing basic respect for your host's faith. However that's not what happened here, what happened here is he went to his sister's for holiday dinner and got all of this shoved in his face with no warning, and then she sniped at him for not doing exactly what she expected without being asked. So he's definitely not the one in the wrong here.