It would be, since it's not on the blockchain. But the purpose of the blockchain is to prevent people from giving you some coins, then giving else the same coins. If they just hand over their wallet, they could hand over the same wallet to someone else later.

The recipient could send the wallet's bitcoins to another address right away, but then the sender might as well have done that in the first place.

Still, in the rare case where you need an anonymous transfer from someone you completely trust, this might be the way to go.

I never thought of that, brilliant.