For those not familiar with the argument: If time travel can change the past, then the present also changes. This can happen again and again (see Dinosaur Beach for an excellent story on the subject), until some random grandfather biting the dust prematurely means the time travel method is no longer discovered. A "no time travel" state is the only stable history, and will therefore become the only one that exists.
And he concluded with a flourish—the kind of thing Hawking could get away with in the Physical Review. He had more than a theory. He had "evidence": "There is also strong experimental evidence in favor of the conjecture from the fact that we have not been invaded by hordes of tourists from the future."
Of course you might ask whether UFO's were visiting from the future instead of Proxima Centauri.
FWIW, there are some features of quantum mechanics that seem to allow states that are a little ambiguous about time. But even if that's what they turn out to be, at human scales you wouldn't notice. h is small.