Don't forget the X-Files spinoff The Lone Gunmen. During its pilot episode, first airing March 4th, 2001, members of the U.S. government remotely hijack an airliner and try to crash it into the World Trade Center, blaming anti-American terrorist groups in order to start a new global war on terrorism for the profit of defense industry contractors.
It may also have contributed a bit to the planning - HEAT (the movie) came out before the North Hollywood bank robbery and shootings, but clearly influenced them. I don’t think there is any plausible direct relationship, just zeitgeist/influence.