That, or (assuming traveling back in time becomes possible someday) time travelers from the future are good enough at time travel to not get noticed. Notice that all I said was "good enough to not get noticed" because we have no way of knowing in this timeline if our history has changed due to temporal tampering.
Doesn't seem possible. If it was one dude doing it once, then maybe. But once it exists, it would get used enough times, over long enough a period, that it would be impossible not to screw up. Someone accidentally dropping something, getting hurt/killed and leaving evidence, a disease (or immunity) that ends up out of sync, etc.
Might start off expensive/secretive/controlled/etc, but what about once it's been around a couple hundred years? Would be accessible eventually. Even if it were repressed for a while, it would pop up again sooner or later.
Think about it: not going to get an even distribution of travellers, and they're all going to want to see the 'big' events, right? At what point are there so many people wandering around Bethleham that there's nowhere for Jesus to actually be born? Would the Titanic sink because of the iceberg, or the 50k people that showed up to witness it? Wouldn't Crazy Horse turn the hell around if he saw that Custer appeared to have another 100k troops when he started his charge?
Pretty much the only argument you need that time travel (to the past) is impossible is that you don't already have proof that it exists. Even if we live in a 'boring' time that no one wants to visit, there'd be evidence of travellers from some other time in the past. Modern human bones in the Le Brea tar pits, or some such thing. Given enough trips through time, it's impossible to avoid.
Can't even play out a DTI or Timecop scenario where they clean up the mess, because every time the time traveller screws up, it changes the future instantly. The timecop now exists in a timeline where that screwup is part of history, and likely led to earlier investigation of possible time travel. Why would he want to travel back in time and try to delete his own history?
Not. Possible.
Ever