What if you'd simply said no in the break room?
When they're forced to repeat the same apology over and over, I kept wondering why the hell they complied? As far as we can see, there's no threat of physical violence, or any other reason to keep repeating it other than the guard telling them to do it. So why even bother playing these mind games at all?
Personally, I know I'm such a stubborn guy that I would have flat out refused to read it any more after seeing what it was the very first time. And the more they tried to push me, it would only encourage me to resist even more.
If they'd actually threatened to hurt me or the people I care about, that would have been a whole other matter... But going along with such an obvious mindless power play over and over just because they ask? That's a big NOPE.