Just like the power dudes cause power things to happen because POWER MAGIC (i mean science) by being in a room, maybe...I dunno, maybe they have some weird POWER AURA that fucks up the oxygen generation process? Because your ship has to be creating that stuff through science magic, I can't figure any way around that.
Maybe one of their cellular respiration pathways in the presence of oxygen gives off a 'harmless' byproduct of ozone from oxygen?
Or maybe their bodies somehow twist O2 molecules into a strange configuration that others can't process? I don't know how, mind you, but I don't actually understand how aforementioned power-magic-auras work either.
Also I'm going to nitpick you: is it that they don't breathe it, or that they don't require it for their functioning? There's a difference.
Not to pick on you LTK, but I'm not sure this isn't a case of simply not twisting your science-fiction logic out far enough. I'm sure we can bullshit up some more silly answers given time.