Read Uncommon Carriers, by John McPhee, which contains the essay "Out in the Sort" [0]. UPS actually does do some 3rd party fulfillment and warehousing. The essay doesn't go into too much detail, but I get the sense that they're targeting smaller volume, higher margin customers. I further get the sense that they're doing so on the basis of being able to deliver small quantities of an item anywhere in the country ASAP while keeping required inventory levels low (because they do the warehousing near their hub).

N.B. It's a 14 year old article at this point. Things may have changed.

[0] Or if you're a New Yorker subscriber: https://www.newyorker.com/magazine/2005/04/18/out-in-the-sor...