Personally I think there's a decent possibility that whoever was manning the radars that night was in on it somehow. It's a crazy idea and it's not too likely, but no other possibility seems particularly likely either. It does neatly explain how the military "ignored" an unauthorized intrusion into their airspace as well as why they "didn't notice it" for some days afterwards.

I'm not too serious about this, yet at the same time it seems like the least improbable idea.