It is completely possible that Cheney did 9/11 because I watched a brilliant documentary the other day by the name of Cheney’s Law all about how he spent the majority of his time in office expanding executive power and finding ways for presidential power to go unchecked by Congress, so he worked with Dave Addington, Alberto Gonzalez, and John Yoo to achieve these goals.
Throughout history, a national crisis like the beginning of a war or an incident like 9/11 has allowed the president to expand his power with little resistance from the judicial or legislative branch, even in the case of a divided government (as it was during Bush’s presidency). Although Bush was president during this time, the majority of important decisions and orders came from Vice President Cheney’s office (as stated in the documentary) instead of Bush’s office, which is highly unusual. While a lot of 9/11 conspiracies are centered around the concept of expanding presidential power, they point to Bush, not Cheney. Bush lacked the leadership style needed to pull off such a feat, but he succeeded in securing political office by using his interpersonal skills (if you’re interested, watch a documentary following him on his campaign and it becomes evident).
Cheney’s aggressive advances on legislative oversight make it easy to believe that he was willing to go far enough to cause a national crisis himself to give him the opportunity to authorize Bush’s wartime powers as commander in chief and declare a “state of emergency”. In 2003, Cheney maintained that his office did not have to abide by an executive order that significantly decreased secrecy in the White House, and he was known for keeping the majority of his affairs in office between himself and his lawyers/OLC employees. There’s a whole lot more to add to this theory, but it could be totally possible.