No, NASA is not part of the USAF. They are a private agency that gets to play with USAF toys.
And Moffett is prettymuch open for business to anyone that can give NASA a bit of publicity and teach somebody something about something. Hence why the farking Mythbusters spend so much time there.
NASA is commoditizing a scarce resource (a no-questions-asked controlled airfield that isn't busy as hell) for their own benefit. Google gets to park their planes near "home base", under very secure conditions, in a place that's easily usable (no takeoff and landing queues). Good for the Googlians. NASA gets to strap some sensor packs to the wings of some toys that they can't afford and they can't borrow from the military (because the military doesn't own many unmodified 767's - they're all tankers or AWACs birds, and they only own a handful of Gulfstreams to move around politicians and generals).
And to top it off, they get cash. It's not like they're using the capacity. It's not like they're selling a parking space for the space shuttle or something.