If I'm the shooter it's ok to say "I think I fouled" and hand the ball to the other guy... first because the shooter is even closer to the shot than the ref so he's more able to call it, and gets some input the ref doesn't (e.g. the feel of a double hit). Second because the instant the shooter picks up the CB and hands it to the other guy, he has DEFINITELY fouled, so it's almost irrelevant anyway. The ref will likely not be offended, because he knows the shooter has a better chance of spotting the foul and will see it as integrity.
It's a little trickier though to call "not-a-foul" on another person. Especially as the guy in the chair. You can't just literally hand it back and give up the inning that the ref gave you. You can't just tap the cue ball and say "it's yours". Then you're giving ball in hand instead of the position the original shooter played. You wanna do the right thing, but giving up BIH when the other guy did nothing to deserve it is overdoing it. Also the ref is going to feel more offended that a guy in the chair thinks he saw it better. You don't antagonize the ref.
I guess both players could do a gentleman's agreement where the chair guy taps the CB, and the incoming guy plays it in position.
It's a little trickier though to call "not-a-foul" on another person. Especially as the guy in the chair. You can't just literally hand it back and give up the inning that the ref gave you. You can't just tap the cue ball and say "it's yours". Then you're giving ball in hand instead of the position the original shooter played. You wanna do the right thing, but giving up BIH when the other guy did nothing to deserve it is overdoing it. Also the ref is going to feel more offended that a guy in the chair thinks he saw it better. You don't antagonize the ref.
I guess both players could do a gentleman's agreement where the chair guy taps the CB, and the incoming guy plays it in position.