Thrawn is an unusual example. He's an exiled Chiss, and was a Grand Admiral after rising in the Imperial ranks as an adoptive Imperial, not as a representative of the Chiss. The Chiss on Hoth are part of the Chiss Expansionary Defence Force, which Thrawn was a member of and was exiled from for violating Chiss custom against preemptive strikes. I haven't seen anything to indicate an origin for player character Chiss, so they could be exiles, diplomats or members of the Expansionary Defence Force.
The Chiss as written in Outbound Flight, set during the Clone Wars, know about as much about the galaxy outside the 'Unknown Region'/Chiss space as the rest of the galaxy knows about them. It seems pretty unlikely that a species like the Chiss would forget even 3000 year old history, hence bending canon for the in-game Chiss. Plenty of what's in the Zahn books has been contradicted by further canon anyway, though; that's the magic of the EU.
Ah ok, didn't know a lot of that. All I read about Thrawn so far was the Thrawn trilogy. It does seem a bit unlikely that they would forget so much about the rest of the galaxy. But then again, I haven't seen many Chiss so far, they seem to be rare.