The context is as follows.
I say that X is true. The (dismissive) response I receive is "Anyone knows that". Is that a complete sentence? Yes, it is grammatical. Yes,it has some semblance of meaning.
Firstly: most people wouldn't see a problem — they would interpret anyone as everyone without thinking about it. But, as other discussions in this forum note, anyone and everyone are not precise synonyms.
Secondly: by inferring an implied set of people, the sentence "Anyone knows that" makes sense, e.g., "Anyone (you could possibly ask) knows that." I agree that most listeners/readers would make this inference without thinking about it.
But note that this interpretation of "Anyone knows that", is only an example. There are other possibilities for implied sets of people. Therefore, it seems to me that if the meaning of anyone is intended to mean all, the sentence is incomplete. What do you think?