I generally unpack "X should have known better than to believe Y" as a way of burying the assertions that X believed Y and that Y is obviously false into the "tail" (that is, the de-emphasized part) of a claim, with a status-challenge tacked onto the front as bait.

This is a common rhetorical technique when people want to direct skeptical attention away from an assertion; the hope is that others will respond to the bait (in this case, the status challenge) and let the assertion go by unchallenged. For example, the hope is that a discussion will ensue about whether or not it's really true that X should have known better, which implicitly concedes that X believed Y and Y is false.

It tends to be a warning sign for me... when someone uses a construction like that, I try to remember to pay particular attention to whatever the bait is distracting me from. Did X really believe Y? Is Y really false? Has the speaker actually given me any reason to believe those things?

This is similar to the urban self-defense principle that when something really dramatic happens down the block, that's a very good time to take a step back and look carefully around you for potential threats.