As I understand it, the mainstream interpretation of that document is not that Bin Laden is attacking America for its freedom; rather, AQ's war aims were the following:

• End US support of Israel (also, Russia and India)
• End the presence of US troops in the Middle East (especially Israel)
• End US support for Muslim apostate dictators

See, e.g., this wikipedia article, or The Looming Tower. Eliezer is correct that AQ's attacks were not caused by AQ's hted of American freedoms.