Is there any difference between the original post and simply sending the private key for an account? i.e. the blockchain does not know this account changed hands?

I was thinking about this a while ago, but it seemed to me that the sender could say buy a space pizza by sending his key to the pizzeria, and as long as the pizzeria doesnt spend the coins, the pizza customer could decide to keep his coins (since he still knows the private key).

I was thinking about a kind of mutual oblivious transfer preventing this? is this possible?