They say that it's possible because it avoids any big paradoxes, but time travel is a paradox in of itself. For example: if someone was to send a message to the past, then we would already have known it, because, by Back to the Future law, only the time traveler is aware of the changes in time that he made. But if there isn't a time traveler, there's nobody that's aware of the change, and it's like it never happened.
Who knows, maybe next week, they'll send a message to the past that reveals the LHC as a potential time machine, and that's how we discover that it is.