Watching this episode again, and pondering the oddity of an entire planetary population transplanted into their own past, it occurred to me that...maybe they weren't.
Is it possible that perhaps the people were actually deposited into a (for lack of a better term) "holodeck" of sorts? More specifically, like the Moriarity-in-a-cube situation.
Why not? Because time travel is more far fetched or impossible than living a life inside a computer?
And, as for paradoxes, these people probably didn't care what paradoxes they might create, just so long as they were alive.