http://en.wikipedia.org/wiki/Controlled_Demolition,_Inc. says it took 12 pounds of explosives to demolish a 2,000,000 pound tower.
1/10 of a ton (200 pounds) of explosives is a staggering amount in comparison. The energy involved in the building falling down swamps the explosives by such a large degree that you couldn't even tell the difference.
Remember that the fire did the same thing that a controlled explosion would do: Weaken the central support. The fire by softening the metal, an explosion by cutting it.
A controlled demolition does not actually explode the building, all it does is weaken the support, and gravity does the rest.
How are you sure that they wouldn't be able to use "more than enough" explosives though? 1/10 of a ton of TNT on each floor, sounds like a lot...but doesn't sound like an enormous amount.
Can you put that in terms that a layman may understand?
Thanks.
P.S. I would love more details, so that I can properly refute these claims based on physics and facts - than just based on philosophy and intuition.