Its a pretty basic rule, and I'm amazed they've fallen foul of it.
It is something that comes up fairly often during the January transfer window - a player signs for a new club between an FA Cup third round match and a subsequent replay, and isn't eligible to play in that.
Ah, okay. I see what they've said - he wasn't actually 'cup-tied' at all though. As far as the competition rules go, he would have been entirely eligible to play for York in the FA Cup, but for the terms of his loan from Barnsley forbidding him to do so.
His loan had been terminated, at the time of the replay.
He wasn't actually cup-tied - he hadn't featured for York in the FA Cup. It is simply as you say, that he was registered on loan at York, at the time of the original Barnsley v Horsham game, and you are only eligible to feature in any FA...