It makes more sense to have trademarked the word as it refers to the company, such that another company couldn’t start saying, “What can brown do for you?”
They have only trademarked the specific shade of brown they use (Pullman brown), and primarily to prevent other shipping companies from using it to create what is called “market confusion.” It doesn’t prevent anyone from using the color brown—unless it can be shown that it is to take unfair advantage of UPS and its reputation.
This is similar to T-Mobile “owning” the color magenta. In this case, you cannot use T-Mobile’s shade of magenta if your company is in the tele-communications sector.
You can trademark a specific colour in a specific context. For instance UPS can trademark that exact shade of brown as used in the livery of a shipping/delivery company. But if someone wanted to use that same shade for something entirely different, or use a different shade of brown, that would not breach the trademark.
When a company receives a trademark (aka Rights protection for use in trade), ever element of the design is covered under the trademark. Color, shape, style, design, layout, typography, etc.