Could I have installed it when I installed special software so I could view my back MRIs?
That's a possibility, particularly because I seem to remember you having mentioned platform problems with the software, but that was a while ago; could oyu have overlooked it for so long?
Yes.
Then I'll go with its likely being associated with the MRI software. (Any chance you can find the thread in which it was discussed?)
Just to clarify, did you get the OSXFUSE pop-up when you were still booted into your recovery partition or after you booted back into OS X? (Edit: The presence of OSXFUSE in System Prefs has led me to assume the latter, nor do I think that there's any way for3rd party apps to run in recovery mode.)