The best he could do was leave the door open slightly by saying that we still lacked a quantum theory of gravity and so anything is still possible. None of the laws of fundamental physics, classical or quantum, forbid travel back in time. In fact they do not even distinguish backward from forward. Time irreversibility is implied by the second law of thermodynamics, but as Boltzmann showed over a century ago, this is a statistical effect of the large amount of randomness present in the many body systems that constitute macroscopic objects. On the quantum scale, however, reverse causality actually seems to be taking place.
Experimental results depend on future conditions as well as the past.
When that restriction is relaxed, most of the paradoxes disappear. Physicists have known for some time that time symmetry provides a ready solution to a great number of the puzzles of quantum mechanics. John Bell, for example, recognized the possibility but rejected it. This is the famous grandfather paradox . However, it is not commonly known, even among physicists, that the time-travel paradox does not occur for pure quantum states.