Yes, Area 51 is an AF base but CIA has paid for most of the planes that were tested there in 50s, 60s and 70s. U-2 was paid for, in a large part, by a CIA budget [0]. Same goes for Lockheed A-12, a predecessor of SR-71, which too was paid for by the CIA [1]. Then there's Have Blue, a predecessor of F-117 which, too, was paid for by the CIA. CIA also paid for a slew of other planes and prototypes which ended up either destroyed or as other AF planes. So while it was an AF facility, CIA had a large say in what goes on there.
CIA also has a large staff of psychologists and other sociology experts who can pull off various deceptions and spread propaganda to a large part of the population. UFO mythology was probably created by them. AF don't have many experts in this area.
[0] https://en.wikipedia.org/wiki/Lockheed_U-2 [1] https://en.wikipedia.org/wiki/Lockheed_A-12 [2] https://en.wikipedia.org/wiki/Lockheed_Have_Blue