I don't think George Smoot is arguing that "the real Universe must be consistent".
He's certainly not arguing in a Theory of Everything sense; if he was talking about theory, he would have said it differently.
He's discussing whether measurements must (if properly done) be consistent: If you measure some single quantity multiple times and/or in multiple ways, all done properly, "consistency" means you get the same result each time.
Physicists tend to believe that there really is a there there: That the Universe is in some sense "real" and exists whether we understand it or not, that it operates/behaves/acts on it's own. If the Universe really is a thing, then that thing has to be consistent with itself: there just the one of it, and our measurements are looking at the same thing over and over.
That sounds so obvious that it's hard to say clearly, so let's consider a different case: They Universe is just some values stored in a Really Big Computer that's doing a simulation. Well, in that case, maybe there isn't a single value to a measurement, because the simulation isn't exact, or only gets more exact as time goes on, or values get updated as the simulation works along. Then maybe measuring the same thing multiple times will get you different values.