I'm not sure what you mean by the "Elements Organizer MOV functionality." The Organizer does at least a dozen things with MOVs -- and I've never heard of a conflict with iTunes.
In fact, it's recommended in the program's instructions that you ensure you have the latest version of Quicktime to run the program, so I doubt iTunes would cause a conflict.
Can you be more specific with your issues?
And, since MOV is just a wrapper which can house any of several codecs, can you be more specific about which videos are showing these problems? What kind of camera or camcorder did they come from?
Yes, very easy. Add to Premier Elements a couple of MOV files (with iTunes closed), then press play and you can see them played. Now, close Premiere Elements, open iTunes and reopen Premiere Elements Organizer and the Organizer will refuse to play the MOV because of some error with codecs and advises to install the quicktime afresh. I have the latest quicktime.
This is very easily reproduceable.
My solution is to convert all movs to wmvs.
Might be worth contact Adobe about this.
You can reach them by clicking the Contact button at the top of this web page.