Stamping one's own form? I'm certain that would have landed said crew member in jail for a night or two, with loss of passport (and therefore loss of job.) I am reluctant to believe that one happened, since everyone would already know who the culprit was.
But the second scenario is plausible. I have noticed that the Customs Officers that collect the Global Entry forms are now taking the time (at least with crew members) to compare the name on the form with that passport and compare the face with the photo. That started about a month to six weeks ago, or at least that's when I began to notice the closer scrutiny.
As annoying and "Barney Fife" as the Customs agents' game is, it is better to play it by the rules. They LIVE to take that bullet out of their breast pocket and shoot someone, and they get triple-credit if it's a crew member.