Likely too late for it to matter for OP, but for future people in similar situations that stumble on this thread,
this seems like one of those situations where "you dodge the first bullet, there will be many more bullets that will follow, and you cannot dodge all of the subsequent ones, so you might as well take the first bullet head on which will be practice for you to take each gradual following bullets better each time around".
So in your case, you can only have so many upset stomachs before that excuse will not work for you anymore. As they will be more and more "team meetings" later in life and in your career.
^^^ Gibberish ^^^
Enjoy any good things, even the little and menial ones, as you will never know what impending distresses could descend upon you in a moment.