KJUmp pointed out to me that I forgot one scenario.
Lone runner on 2B is the Base Umpire's call.
I'll also mention that the only time any of this changes is if the Base Umpire goes out to call fair/foul (which should NEVER happen when the Base Umpire is in B, or I'll f'ing smack you), or if the Base Umpire goes out to call the catch/no catch.
General rule of thumb is that if the Base Umpire turns his/her back to the infield, the catch/no catch is now his/hers. However, if you're the Base Umpire and you do this, do it right: GO OUT THERE. Make it clear to your partner that you're going out to make the call by calling out "one man" or "going," and move your butt out of the infield to make the call.
Sorry for forgetting that.