I think it would be more accurate to say that he has an obsession with cooties* rather than a compulsion. IIRC, the way OCD works is that the person is obsessed with something, and consequently feels the need to perform some sort of action that he/she feels will solve or prevent the problem. For example, there are people who are obsessed with the fear they may forget to lock the door when they leave the house. Therefore, they develop the compulsion to lock, unlock, and relock the door fifty times.
The reason I’m doubting it’s real OCD (assuming the gossip has any merit to begin with) is that Gore himself isn’t performing any compulsory behavior. He’s asking someone else to clean the towels for him. If he truly was obsessed with cleanliness, would he entrust anything to someone else’s grimy mitts? Doubt it.
Besides, given some of the hotels I’ve been to, I don’t blame him for asking for re-washed linens.
*[sub]Isn’t the whole cooties thing a dead giveaway that this story is probably untrue?