"Schism" is not that rare of a word. Fucks sake, Anthrax titled a song "Schism" back in '88. Tool recorded a song called "Schism." Clearly it's not just the province of stuffy professorial types.
Also, if you can't tell Jared Allen is being sarcastic in this video, and you're an American, you prove my Euro friends right: we can't tell sarcasm for shit.
Reading this here article reminded me of when that douchewar Fred Durst caught flying screaming crap for using the word "agreeance," or the disbelief over Roger Clemens' claim that someone sometime "misremembered" something. People were aghast: those aren't words! Except they are. (I actually use "misremembered" in No Setlist, in a review that predates the Clemens steroid saga.)
That's why I love words. You can confuse people with them.