It's complete, utter, nonsense, with absolutely no room for equivocation.
Remarkably, there's never been a thread where anyone has tackled this subject and given a serious debunking. The most relevant threads are this one, this one (not specifically about PT, but a related crackpot theory), and this post (which links to an article that debunks it). These threads treat the subject with the lack of seriousness it deserves, so we really have no serious debunking in an AskHistorians post. Many regulars here could make a compelling debunking, so I offer a selection of points below; but it would be nice if someone were able to come up with a really crushing debunking that could go in the FAQ for posterity.
So, a selection of points:
- records of pre-911 CE astronomical phenomena conclusively disprove PT
- dendrochronological dating of pre-911 CE archaeology conclusively disproves PT
- soil accumulation analysis of pre-911 CE archaeology conclusively disproves PT
- carbon dating of pre-911 CE archaeology strongly weighs against PT
- PT is totally Eurocentric; historiography from other parts of the world are ignored, including records of astronomical phenomena
- the arguments adduced in favour of PT are based on hypothesised possibilities, not on evidence
- PT posits an intentional conspiracy on a continent-wide scale in the mediaeval period, and an intentional conspiracy on a worldwide scale in the present; this is both insane and impossible. Supposed evidence for this conspiracy is claimed to lie in the fact that the chronography of mediaeval and ancient history is difficult.
- PT claims support in the institution of the Gregorian calendar, and claims it was supposed to synch up with the Julian calendar when it was first instituted in 46 BCE; there is no reason to suppose this. (In fact the Gregorian calendar was designed to set the date of Easter properly, and it synchs up nicely with the Julian calendar as it was when the date of Easter was fixed, at the council of Nicaea in 325.)
- PT lays an enormous amount of weight on architectural styles as a dating tool; that is a rotten dating method
I'm sure that will do for a first approximation, but as I said there's certainly room for a really crushing debunking from someone who's actually looked into PT in detail.