Yep. Catch-22.
Excellent point 4WB.
In additional to hypothetical memory, ptsd memory, exaggerated memory, and the actual fogginess of memory, the NCIS comes in and keeps these guys in a room with a bare bulb, withdrawn freedom/food/bodily function relief, threats, pleas, deals, and the psycho-techniques taught at interrogation school, and then they get their scribble on a "statement" sheet.
Just a little of that when you're groggy from too little sleep, and you'll confess to being the guy on the grassy knoll.