As I understood the article, he's neatly sidestepped most of those proofs with his definition of "the flow of time". He agrees that certain properties are associated with their direction along the time axis (e.g. entropy increase in the futureward direction, memories are only available of pastward events). Is suspect that he would also argue that throwing out the anti-causal solutions to the wave equation is nothing more that customary, and that Merlin and Chris Nolan would customarily discard causal solutions and keep only the anti-causal ones.
What was frustrating for me was that he didn't seem define "the flow of time". I would have defined it as the idea that the universe is not translation invariant along the axis measured by clocks. The truth of that statement is practically tautological, as he already agreed that clocks do measure intervals and that measurement inherently breaks the translation symmetry. Then again, cosmology isn't my field so maybe I'm missing something.