It's not NBC who's making this claim; they're simply reporting on what the guy said, which is quite different from actually confirming the claim. This is an extraordinary claim, one which would need a substantial amount of proof to back it up. This guy had no proof from what can I can tell, and seems to be bullshit. It reads as if it was taken out of a sci-fi novel. If in a decade aliens start undeniably appearing and we're all proven wrong, then whatever. But for now, I'm taking this claim with a boatload of salt.
Also, I find it extremely hard to believe that Trump would be one of the only humans to know about aliens and not immediately furiously Tweet about it.