I understand that. However, the process is the same for everyone. If, on a single day, I receive a cheque, I deposit and I write a cheque, I agree that my institution may not have received my money from the other organization. But it hasn't given away my money either. So there's no reason for it to collect interest during that period. The same rule should apply on both sides.
I don't see how they can immediately withdraw the money from my account, then give it later, and collect interest because they haven't yet received the money which is probably still being held somewhere in an intermediate account elsewhere.