BTW I don't disagree with what you just said - was just trying to explain this middle bucket because I don't think it's a clear no. Sometimes (very rarely) those middle bucket interactions turn into funding. But I agree w/ you that it's usually a waste of time.
The logic is simple - if the original VC is waiting for a new VC to get excited about it, it would not matter if the original VC is still in the mix or not (as the entrepreneur now has someone else interested). If no one else gets excited, spending time on the original VC is a waste of time, since she won't tip unless someone else does.