James has alread discussed one of the problems with the claim that the buildings fell as fast as if they'd been in free fall, namely that Avery estimated the free fall time based on the height of the roof, when in fact the buildings collapsed from where they were hit.
There's a rather simple way, though, to show that the buildings did not come down in free fall. Here's a screen shot from Loose Change at 9:57, showing the collapse of the South Tower:
What do we see? Think about the World Trade Center and the debris falling from it as an umbrella. Here's another shot that gives you an idea of what I'm talking about.
What is clearly evident in both these photos is that the debris field in general is falling faster than the building. This creates the umbrella effect. In spots where there is visibility through the debris field we can see that the building is intact higher than the debris. But if the debris is falling faster than the building, what does that mean? That the towers did not come down in free fall. They came down fast, to be certain.
Update: Commenter CV-PHD points out this section (PDF file, see page 196) in the NIST:
I still say the above photos show that the building was not coming down in free fall, but since the experts say it was "essentially" free fall, this seems to be a minor point; someplace where the experts and Loose Change are "essentially" in agreement. I guess the obvious question is how fast do buildings that are being demolished come down; do they come down in essentially free fall as well?
It is argued here that the collapse time is more like 15 seconds while free fall would have been more like 9.2 seconds. In an oddity, Loose Change purports to clock the time the building took to fall (at 35:55 of the film), but they don't show the total time; instead the clock fades out after measuring about 10.23 seconds:
(Click on picture to enlarge; you can barely see the numbers 10:23 in the bottom center). There is an open question as to whether Avery started the clock at the right time as well; looking at 35:55 in the movie it certainly appears that the time is close to 10 seconds, but check out the earlier view of the collapse at 35:22. The collapse is clearly underway (note the top of the building leaning slightly to the right). Now just watch the film and check out the running time. At 35:32, when the building should be completely down according to Avery, we can see that it's still nowhere near the street. Indeed, the debris field (which was ahead of the structure) is now only at the level of some of the rooftop of some of the smaller buildings:
Indeed if you watch the version of the collapse at 35:22, it appears to end around 35:37, which fits pretty neatly with the 15 second estimate by 911 Myths.