Since this is already an improvement, I'm attaching a patch.
If on the other hand, someone is pasting into psql's terminal a block of commands enclosed in BEGIN/COMMIT, the same bug is triggered: BEGIN doesn't have effect and the rest of commands run outside of transaction.
Is it possible at all to protect against the latter case? How?
One idea I was just suggested is to make interactive psql sessions buffer in all available input, before it's going to block. This way it doesn't matter if the multiple statements are appearing on one line or are being pasted.