From the sound of it ATC applied visual separation at the last minute, even though the pilot accepted it there isn't any time (only a mile at most) for the GA to out manuever the B777 that's climbing through his altitude. Almost seems like local applied visual separation as a CYA.
I didn't wanted to comment to this, but I can't resist

A GA usually can turn around it's own axis in a short distance, this Cessna needs only 200 to 300 feet, doing a full 360 if they have to, but that depends on pilot skills....
