@proedie @riley given a cursory googling and this reddit poll, it doesn't seem like the meaning is that clear to the average person
https://www.reddit.com/r/polls/comments/1brhoj4/how_do_you_interpret_the_saying_a_broken_clock_is/
@proedie @riley after obsessing a little over getting to the bottom of this, the answer seems to be that the historical origin (from 1711) is akin to "If you stop chasing trends you will sometimes be fashionable", which is more in line with riley's definition in the OP. The other "official" definitions I've found seem to follow this as well.
The definition that "coincidental correctness is worthless" seems to be a personal (though common) interpretation.
@jonoleth @proedie @riley I always thought of the saying in re those people (often conspiracy theorists) who are singularly obsessed with one thing and always turn to that thing as their explanation for the whole world around them. Occasionally their obsession actually will be the correct answer but it's not like you gain any insight from listening to them.
It's not an acknowledgement of their insight, but a wry and half mocking acknowledgement that today, for once, they get to be right.