I'll sprinkle some thoughts on this topic, as I've given it a bit of consideration lately.
I am, and am not, a partner.
Any huge institution such as UPS has a certain amount of institutional inertia that carries it forward - no single person, despite how highly they may think of themselves, is indispensable; the institution will simply carry on by repetition, force of habit, and other such things. In that sense, I am not (and perhaps no one really is) a partner.
On a more practical level, consider the building I am employed in - as aforementioned, I'm not indispensable, but I believe that I make a difference for those I supervise and for the multitude of folks who happen to constitute "my boss". There are good days and bad days, but by and large I always do my best and I feel that I am good at my job. In this way, I am a partner in the sense that I am a member of a partnership interested in conducting business. They may not all recognize it as such, but that is how it seems to me.
On the management level that is removed from the "center" level, no, I don't believe I am a partner there and am quite sure they don't regard me as one, either.
Strictly defining "partner" as an employee of UPS who receives securities compensation may be historically or technically accurate, and I may be speaking of things I don't know for saying this, but I think it misses the point: to make an employee feel valuable, that their effort makes a difference and is recognized (be it through compensation, a holiday turkey, or whatever) ... that feeling and confidence that what they sacrifice is appreciated, is what it means to be a "partner". To that end, I imagine every good driver (or hourly) should be considered a partner, as well.