Some airlines, particularly SWA, FDX, and DAL all seem to have historically liked military pilots, and if anything put a "halo" around some. UPS interviewers have often appeared to have more of a "well..these guys didn't have the taxpayer pay for THEIR training..." type mindset.
There are plenty of good pilots from all backgrounds at UPS, but I know quite a few military interviewees shown the door. A couple are now at FDX and one at Delta. Being military at UPS was "no big deal" to the interviewers.
Conversely, I've seen guys who "weren't FDX/DAL" material hired successfully at UPS.
All this makes me think if you have been schlepping freight in ****-holes around the world, or working 135 somewhere, UPS does NOT look down on that but rather seems to respect the grit you have shown. What made you feel "less sexy" at your Delta interview is actually an attractive trait to UPS.