Boats can be searched for safety and fishing/game inspections, your person is really the only secure thing there. I have no idea about the case law on aircraft, but most of that is probably federal..
Aircraft searches fall under the same requirement for PC as any other conveyance, barring being at a Functional Border Equivalent as your first landing point when entering the US (airport of entry), then it's the same as being searched at the border. That's for search. For simple document check, 14 CFR 61.3(l) provisions apply.
Insofar as something you possess being under a gag order or NDA, wouldn't there be some sort of official paperwork accompanying it that would identify it specifically as such? Otherwise I would think that anyone could make that claim willy-nilly about anything.