The elector may have secretly intended to vote for John Ewards, but the joint session judged this to be a vote for John Edwards. So technically, Edwards won that electoral vote.
Which was especially insane as the Constitution explicitly bans electors from casting both their votes for the same person.
That's not correct. The recipients of the votes for President and Vice President cannot both be from the elector's home state. So an elector in North Carolina could not have voted for John Edwards for both offices. But someone in Minnesota can.