Thanks for pushing for clarity here. So: I'm not saying that fact-checker warnings are ineffective because people just click through and ignore them. I doubt that they do; I assume the warnings "work". The problem is, only a tiny, tiny fraction of bogus Facebook posts get the warnings in the first place. To make matters worse, on Facebook, unlike on Twitter, a huge amount of communication happens inside (often very large) private groups, where fact-checker warnings have no hope of penetrating.
The end-user experience of Facebook's moderation is that amidst a sea of advertisements, AI slop, the rare update from a distant acquaintance, and other engagement-bait, you get sporadic warnings that Facebook is about to show you something that it thinks you shouldn't see. It's like they're going out of their way to make the user experience worse.
A lot of us here probably have the experience of reporting posts to Facebook for violating this or that clearly-stated rule. By contrast, I think very few of us have the experience of Facebook actually taking any of them down. But they'll still flash weird fact-checker posts. It's all very silly.