Happily, I’ve never had to rule on a situation like this.
I can see two ways this could have happened without either player deliberately cheating:
Scenario #1:
White saw that Rc5 would be a blunder but that Rc6 would be a reasonable move, chose Rc6, but incorrectly executed the move, placing his rook on c5 instead of c6 (though he correctly recorded the move he intended to make). This scenario seems extremely unlikely, since we must presume not only that White misexecuted his intended move, but also that he failed to realize that he had placed the rook on the wrong square, pressing his clock button and recording his intended move without realizing it wasn’t the move he had actually made. Since players don’t need to visit the bathroom all that frequently during games, we would therefore have to presume that three unusual things - misexecuting a move, failing to realize the error as soon as it was made, and needing to visit the bathroom - all occurred at the same time, which is very unlikely. In any case, the rulebook is quite clear on what should happen: Rule 10G states quite clearly that white must leave his piece on the c5 square.
Scenario #2:
White failed to see that Rc5 would be a blunder and deliberately chose to move his rook there, but mistakenly thought that the square was c6 instead of c5. He was shocked when he returned from the bathroom and saw that his rook had been captured (since he hadn’t noticed the threat) and, noticing that he had recorded his move as Rc6 while black’s pawn was on c5, chose to believe that he had made the move he had recorded rather than the move he had actually made. This scenario is easier to imagine, since most of us have at one time or another misrecorded a move. But the rulebook would (of course) still dictate that the move White actually made (Rc5) must stand, regardless of what he recorded.
The other possible scenarios I can see would both involve deliberate cheating by one player:
Scenario #3:
White moved Rc6, but Black chose to take advantage of his bathroom break and to record White’s move as Rc5 and then move bxc5 in order to gain a winning advantage.
Scenario #4:
White mistakenly moved Rc5, failing to see the threat, but then realized his mistake after he had released the rook on the c5 square but before he had recorded his move on his scoresheet. Realizing that his mistaken move had already been determined at that point, he concocted a plan for avoiding a loss, recording his move as Rc6 rather than Rc5 and then excusing himself for a bathroom break, with the idea that he could protest after his return that Black had taken advantage of his absence to cheat.
My first inclination was to back the game up as Brennan suggested. But this would effectively mean ruling in White’s favor, since White would end up getting to make the move he recorded.
Another option would be to have them replay the move but prohibit White from moving Rc6, though the equity of this solution would depend on whether White had any other safe alternatives. And it would raise the question of whether White should be required to move the rook somewhere or permitted to make any other move he chose.
The most equitable solution might be to simply declare the game a draw, or to forfeit both players (so that it would not affect their ratings). Rob says that double forfeits are “not the best policy for future business relationships” but it’s not clear to me that a possibly unjust ruling would be better policy.
Another possibility might be to void the game and have them play a new game, limited by the time remaining for the round.
Bob