Me and a buddy were playing GRAW this morning (on the same xbox), and I found a pretty annoying glitch. We played co-op elimination against computers, and if he died and then observed me, my y-axis would switch to inverted, and the menu would still say inverted is off. Even when I turned it on it was still inverted. It wasn't a one time thing, it happened every time he died first. Also, he uses inverted controls and I use normal. And if it might matter, we set up the custom game on xbox live, but got impatient, so we just played co-op elimination.

The only solution to this is to avoid observing as far as I've been able to figure out. It doesn't really matter since you're looking at the same TV anyway. I noticed this on GRAW and, strangely enough, on Ghost Recon 2: Summit Strike for the original xbox. Apparantly whatever error they made was not caught the first time.

Edit: I doubt it matters where you set the game up. I did mine normally through "local play" and had the same results as you.