I think its pretty clear in this case that the root of Al Qaeda's hate of America has nothing to do with America's freedom. There are many countries which are just as free--if not more so--than the US. (Has Al Qaeda ever bothered to condemn Japan?) No doubt they disapprove of many aspects of the American lifestyle, but mostly they are interested in signalling to their fellow Muslims the purity of their opposition to US power in the middle east. Attacking a shared common enemy is a tactic for increasing support for Al Qaeda throughout the Muslim world. The root cause of the Anti-American sentiment is the very real history of US aggression and meddling in local affairs.

Likewise, when US politicians condemn rival countries for human-rights violations, you can be sure that they don't actually care about human rights. Hence they frequently condemn Russia, Syria, and Iran while being close allies with countries that are much less democratic and much more oppressive (Saudi Arabia, Bahrain.)