"Parent" option under "Parent Attributes broken – only showing a few pages…

Titele says it all. When I go to create or edit a page, the Parent attribute dropdown under Page Attributes is showing only a few pages. It’s odd because it’s only showing those that aren’t already parents. To add to the confusion, editing a child page automatically removes it as a child and makes it top level.

I’ve tried all the usual, e.g. disabling and then uninstalling all plugins, reverting to original theme, as well as more complicated things like copying the database over to a new install (only the eleven default WP tables) and exporting XML from the working install and importing it into a brand new one. Nothing seems to fix the problem. This is puzzling because I’m relatively experienced with WP and have been working it for almost four years now. Any idea what’s going on?