Hmmm...I don't know. That's a toughie there. I agree that it would be noble of X to step down if he didn't feel he could reign properly, but at the same time, I also agree that it puts Y in an awkward position.
Granted, I'm not really familiar with SCA rules so take this for what it's worth, but I think it depends on the circumstance. Did X go in with the intent to win, but had some last-minute "epiphany" after he had won? In that case, I think the thing to do would to be discuss it with Y and make sure he was okay with accepting the reign instead of just saying, "Y'know what? I don't really wanna be king. It's all on Y now."
Or did he go into the competition with no desire to be king and just want to fight or want bragging rights?
Basically, I guess it kind of depends on whether X had some kind of ulterior motive, or if was it an honest change of heart.
Edit: ninja'd by Sir James.