It has been stated that "The towers, if you notice, did not fall straight down, The top section fell on the damaged section and tilted on an angle, then the lower floors pancaked."

I believe the poster was referring to the collapse of the top of the south tower. That fact is indeed noted by physicist Steven Jones. Apparently in that one instance, a piece of the tower didn't collapse in sync with everything else. Steven Jones noted something quite interesting about this, as he mentions in his article "Why Indeed Did the WTC Buildings Collapse?":
******************************
Those who wish to preserve as inviolate fundamental physical laws may wish to take a closer look. Consider the collapse of the South WTC Tower on 9-11: http://www.911research.com/wtc/evidence/videos/docs/south_tower_collapse.mpeg

[Here is a picture of the event:]

http://physics911.net/images/9-11%20Picture8%20(sotower).jpg

[In the picture, the] Top ~ 34 floors of South Tower topple over.

What happens to the block and its angular momentum?
We observe that approximately 34 upper floors begin to rotate as a block, to the south and east. They begin to topple over, as favored by the Second Law of Thermodynamics. The torque due to gravity on this block is enormous, as is its angular momentum. But then — and this I’m still puzzling over — this block turned mostly to powder in mid-air! How can we understand this strange behavior, without explosives? Remarkable, amazing — and demanding scrutiny since the US government-funded reports failed to analyze this phenomenon. But, of course, the Final NIST 9-11 report “does not actually include the structural behavior of the tower after the conditions for collapse initiation were reached.” (NIST, 2005, p. 80, fn. 1; emphasis added.)
Indeed, if we seek the truth of the matter, we must NOT ignore the data to be observed during the actual collapses of the towers, as the NIST team admits they did. But why did they do such a non-scientific procedure as to ignore highly-relevant data? The business smacks of political constraints on what was supposed to be an “open and thorough” investigation. (See Mooney, 2005.)
So I with others call for an open and thorough investigation. I hope the international community will rise to the challenge. The field is wide open for considering the alternative hypothesis outlined here, due to its neglect by studies funded by the US government.
******************************