Been digging around for an answer for a couple hours, and all the results I am getting are completely irrelevant.
For some reason OpenOffice, in its "Open" and "Save as" file explorer windows, has this "Application Link" that has a link to what is technically my "My Documents" folder. I say technically as my "My Documents" folder is actually a symbolic link to a network shared folder, and so the link, in the "Application Link", shows that folders network share name.
I know that you can remove the "Favorites" and the Libraries" from the "File Explorer", as well as the open and save as explorer, with a couple changes to the registry. And I think it's a safe bet that this can be removed with a registry edit, but finding where it is in the registry is impossible. Also I would assume the value I need to set it to, is not something that can be easily guessed at.