He didn't say that it was logically proven, just that he "reason[ed it] out". That's pretty informal and I think does not need any caveats along the line of "it could exist in such a way that is indistinguishable from not existing". After all, if I reason out that there's no such thing as ghosts, that doesn't mean I'm claiming to have a perfect logical proof that shows that they're impossible, just that according to the evidence it doesn't look like they're real.