> So my peer group made it a drinking game. Every time <my friend> apologizes, everyone has to drink.

Chances are that someone who apologizes for "basically breathing" doesn't have the ability to even express mild displeasure at the game, much less feel comfortable requesting that it stop. So it's a coin flip whether your friend a) feels like part of the group during this activity in a positive way, or b) takes the whole ordeal as yet another reason from the universe to apologize.