Nonsense. Criminals do stupid things all the time. Just in the news as of yesterday, we had a purse snatcher who managed to get his picture taken by the family he was stealing from. I told you faithers how Obama used misdirection to get away with it.
The purse snatcher got caught. If your asserted requirements for NBC status were correct, Obama would be caught red-handed (and no state would put him on the ballot, no elector would have voted for him, and Congress would have refused to certify the result if they had). Ergo, your asserted requirements are inconsistent with the law under which the government actually operates.