You could set it up so whoever initiates a transfer could get a kind of receipt that proves they initiated a transfer of X dollars to whomever. So if Alice tra

You could set it up so whoever initiates a transfer could get a kind of receipt that proves they initiated a transfer of X dollars to whomever. So if Alice transfers 5 dollars to Bob and Bob says "What 5 dollars? What are you talking about?", then Alice could say, well here's my receipt, that's signed by my private key and the private key of the FHE bank, that shows that I sent the money to Bob and the FHE bank executed the transfer.