Do you mean that "cellophane-like" sleeve? Don't be fooled, I had one refurb come with that and I initially thought that I may have gotten a new unit - until I actually removed it and it was scratched to hell. If it has minor damage it is likely due to the previous user.
Yes. If it is not in retail packaging, it is refurbished.
I am not against sending out refurbished units as warranty replacements (within the first month the replacement should be factory new) IF they are actually refurbished to the claimed "like new" condition. Far too many refurbs are in less than new condition. If your refurb is in good cosmetic condition, then it is likely that the previous owner took good care of the unit (rather than MS's efforts). The first refurb I received (and currently using) was in good cosmetic condition. The refurbs that followed were sorry sights and I finally gave up and I am reluctantly living with my battery issue (also, all the other units exhibited the same battery issue).
To make matters worse, the automated exchange process only allows you to specify one defect. My original unit had multiple issues. Of course, I shoehorned my other non-battery related issues into the "battery problems" form. But, units cannot be checked for problems of which they are unaware...