I may be listening to the wrong part (as QT on the browser does not have a timer), but he states that there was a shell of outer columns, then he mentions a 'big structural base' in the middle. Then he states that there is just the floors in between. He then states "THere wasn't like a series of columns in between" (unlike the ESB). He is talking about the space between the structural base and the outer columns. He then mentions that the plane went through the outer columns and did not stop until it hit the core (prior to this he states that the WTC towers did not have a 'thick, concrete core' like the EBS, which is accurate).
At no point does he deny the columns in the core. He simplifies by calling it a 'big structural base'. But there is no statement that there were no columns there.
I don't think he is the one lying here.