Could they tell that from a big ol' nuke? Great is the power of prayer.
Yes, they could. Metor's don't leave a radioactive crater, and no one in the world has that big a nuke anyway.
Now you could just drop a big rock (asteroid) on them, but we aren't quite up to doing that either, although the theoretical aspects are solid.
Just as long as *we* are the ones doing it, and it's not followed by pygmy elephants in pink platform shoes raining down from the sky in hang gliders. :) ("See Niven and Pournelle's, "Footfall"