He makes no mention of the fire proofing. I hope it's mentioned in the show but I doubt it.
As the links posted by others indicate, asbestos was used in the construction of the building, up to about halfway up. Then, during the time the towers were still under construction, asbestos was outlawed, and the remaining stories were built with some "substitute."
It's an open question whether the towers would still be standing if asbestos had been used all the way up. Possibly they may have stood. Alternatly, maybe they would have still fallen, but stood for a longer period of time, thus enabling more people to escape.
Either way, the decision to not continue to use asbestos was a political decision, not an engineering one.