"Soon" might be a bit optimistic.
I think they're wrong about the "Grandfather Paradox" demonstrating that time travel into the past is impossible -- just that it's going to raise all sorts of strange consequences. It's probably some sort of "cosmic censorship hypothesis" instead, which states that the Universe doesn't let us do weird things.
Time travel of a sort might be possible, although with the likely caveat that you can't go backwards arbitrarily, and you'd have to set up the "closed timelike curve" at the earliest point in time rather than the latest. That is, you might be able to say "I want to be able to return to when and where I am now", but it's unlikely that you would also be able to say "I want to see dinosaurs" or some such.
Even if it is possible, "soon" is probably optimistic though!