I believe the player can make a carom off of the opponents balls if it is the object ball that caroms not the cue ball. For example, a player shoots his 7 ball into his opponent's 15 ball making the 7 in the corner. I see nothing in the rules that prevent this type of carom.
BCA specifically states that a legal shot includes:
A: using legal equiptment (checked before the games begin)
B: using a legal stroke (tip first, no double hits)
C: hitting a legal ball first
D: potting the called ball in the called pocket.
A carom off an illegal ball is a foul
A carom off a legal ball is fine
BCA also specifies that the shooter must call any nonobvious shot, and that a safety is a nonobvious shot
BCA further specifies that the opponent (you) have the right to know what the call is, but that you cannot instrrupt the shot
Shooter did not call nonobvious shot: ruling:: end of inning, shooter did not make called ball in called pocket, and did not comit a foul (unless original statement of play was missing in details).