Suppose you are landing in Cleveland. The flight was supposed to go to Buffalo, but was diverted because of weather while you were snoozing. You look out the window and say, "that city is Buffalo". After being corrected, you say, "Well, for I all I knew it was Buffalo." If we suppose that names and demonstrative phrases are directly referential, the proposition you expressed was that Cleveland is Buffalo. This seems like an impossibility (or a very Erie possibility). Then if we suppose that epistemic possibility amounts to being true in some worlds consistent with what you know, your second remark seems false. Or consider the case of Ralph who sees but does not recognize his neighbor Ortcutt on the beach (he's never seen him in a Speedo before) delivering secrets to Igor the well-known spy. He says, not recognizing Ortcutt, "that man is spy" and "I know that man is a spy". Is there a man such that he knows he is a spy? Hintikka, whose epistemic logic requires such a man, says that there is one, but he isn't an ordinary man, but rather a demonstratively-individuated man, consisting of all the modal man-slices that Ralph is seeing in the various worlds consistent with what he knows. We might make a similar move in the Cleveland case.

I will recommend, however, that we handle epistemic possibility in both cases by retreating to reflexive content, which I will describe as best I can.