Just heard that 10% of the first intake of pilots for weapons training in the US failed on the basis of the mandatory psychological / background checks.
There have been conflicting reports. I have heard that 2-4 left the first and only FFDO class ever held. 2 for sure "failed" out due to "backround checks". I've heard that the others voluntarily dropped out for other reasons.
A close friend of mine knows one of the guys that "failed" his backround check. He was ex air force, and held top secret clearance while overseeing the transportation of nuclear weapons. As a civilian, he (along with one of the other guys that "failed" his backround check) was one of the more vocal lobbyists for arming pilots, after the TSA said that they wouldn't do it. They convinced congress to override the TSA's decision, which angered a few folks in the TSA. I find that a pretty big coincidence.
Since the TSA doesn't have to tell you why you "failed", there is no accountability.