It seems to me that when we combine your hypothetical here, my one (and the one in the comments) in the old LJ post I linked to, and Gettier's ones in the Wikipedia page you link to, the common thread is that all of them have a true belief of the form "One of the following set of possibilities is true", with a justification "Specifically, I have reason to believe it's this one". In fact it then turns out that the thing asserted in the justification is false in spite of looking plausible, but fortunately one of the other possibilities in the set is true, and thus the originally stated belief manages to be true despite the justification being wonky.

Are there any examples of this phenomenon which don't have that form?