I've seen this on a few sites now and its puzzling me. The page will be listed under the "Edit Posts" listing, however, when I click on "View Page" to see the live post, its being served out as a "Page". I can tell this by viewing the source and the body tag is...
<body class="page page-id-37 logged-in">
If its were actually a post, the body tag should be
<body class="single postid-63 logged-in">
I've seen a "post to page" and a "page to post" plugin that will convert between pages and posts, however, this site has NO plugins other than the wordpress defaults (akismet and hello dolly).
I'm stumped.