"When there is false information but the the poster is not trying to mislead anyone, that's just someone on the internet being wrong, and there is no Facebook policy against it."
In and of itself, being wrong is not a problem. You can be thwarted by debate and evidence. However, it's much easier to spread a lie than to effectively repute one, so this gets out of hand very quickly.
"This is why Facebook concentrates most of its efforts on the last category, when someone spreads lies with the explicit intention to mislead."
The trouble is that most of the second category is actually the third category. Just because the lies are coming from random people, your uncle Joe, or some innocent organization sowing dissent in the US and secretly run by a Russian, and just because they don't say, "This is what you should believe so that the world can be run by neofascist forces", doesn't mean that the intent isn't to mislead. Any attempt to spread lies and falsehoods via the common viral video or meme styles IS an attempt to willfully spread lies. To assume that much of this isn't willful is naive.
Leaving it to Facebook to decide what's intended to mislead has not been working. The solution is not to trust anything you see on Facebook or to leave the platform entirely.