Is there any other place – besides a theme, a plugin, or a mu-plugin – that an option page might conceivably be used?

Unless you are working on WordPress core development you should not be writing anything but a:

  1. Theme
  2. Child Theme
  3. Plugin
  4. Mu-Plugin
  5. Drop-In

For the last two see: http://hakre.wordpress.com/2010/05/01/must-use-and-drop-ins-plugins/

I am out on a limb a little bit here but I think that is the exhaustive list, with the first three by far the most common.

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