So yep. Exiting out of any playing video or song in WMP will not work, I have to kill the process directly. From my extensive Googling of the matter I've found this is due to Windows Sideshow, which has WMP as a gadget that it does this for. Unfortunately I can't remove it from this stupid Sideshow thing, nor can I edit the settings anywhere for it.
Any idea on what to do here?