Also confused by the “Logan’s Run” reference. It’s been forever since I’ve seen the movie (and I never read the book) but from what I remember, the main character was essentially a cop who was all “crap, I have to stop killing people because it’s all for a lie” which is approximately the opposite of what they’re suggesting here.
“The Running Man” doesn’t really work either; in both the movie and book versions (which are rather different), the main character is killing all the bounty hunters after him, because that’s how the game is played. That’s all for a lie too.
I can’t think of anything where a group of misguided rebels or protesters or whoever were demoralized by a loose cannon going all Rambo upside their asses, or even anything which could be metaphorically interpreted as such. I’m going to guess that they’re both thinking of the wrong movie/book *and* badly misremembering the plot, whatever it is.