I still sort of suspect it's a UI element that's going to be beyond control.
If it is, you could lay out your InDesign pages to minimize it (keep them from appearing between pages, for instance).
Do you have a different version of Reader (or another PDF viewer) to see if it's a UI element, dependent on your version of Acrobat or Wn7? Those don't appear in PDFs I create from InDesign or Illustrator (via postscript->distiller) in OSX, so if we determine that it's an artifact of how you're creating your PDFs, rather than a UI element, I'm sure we can eliminate it.