No one wants to say it for fear of being labeled anti-Islamic, but it was the men's consistent acceptance of the fundamentals of religion that turned them into terrorists.
When you strip away the nonessential details, all religions are pretty much the same. They all rail against worldliness, "materialism," prosperity, and seeking happiness on earth. They all promote self-sacrifice over self-interest, obedience over independent thought, a "supernatural" dimension over reality, faith over reason.
Unfortunately for us, Osama bin Laden and his cohorts do what most religious believers, Muslim or otherwise, do not: they take their faith seriously, as much so as any Christian of the Dark Ages.
The terrorists renounced earthly happiness, obeyed clerics, assaulted a symbol and hub of material prosperity, longed for the supernatural and sacrificed themselves, all the while exhibiting unshakable faith.
Rather than "twisting" or "perverting" religion, it seems as though they practiced its fundamentals unto death.