Oh, I should add, yes, I had it in menus, main screen, pop-ups, etc - once it triggered - and then after some number (one, two, a few dozen) page-turns, it would clear itself. So, yes, I think we have the same problem.
And, yes, my purchase date was in early March 2011 -- that, with the fact that I'm also seeing almost zero availability for the 360(+) models anywhere, worry me. It seems the trend is back to the over-sized 6" models, or worse, LCD / touch devices. None of which come with the clip-on plastic cover. Frightening times ahead.
Anyway, please do let me know how it goes with the service on it. I guess if they decide to replace it, the worry there would be that if they can't replace it now with any residual 360 stock, they'd try to talk you over to a different model?