How did you change the rights? did you make sure the changes only applied for the specific page and not any child pages? have you made sure that the page doesn't link (ex: the menu) to any pages that Everyone doesn't have read access to?

This can happen if either CurrentPage or any page you retreive using PageBase.GetPage() method is in the Wastebasket (unless you are an editor) or you are lacking access rights.

Note in EPiServer 4 that GetPage on DataFactory does throw an exception but it is only GetPage on PageBase, PageTemplate and UserControlBase that catches it and hides what Page ID you are not allowed to see.

You can see the exception (and get some clues) if you create a test user that has no group memberships but have the persmission for function to see error messages. Log in as this user and go to the offending page.