I don't think UPS is making any extraordinary claim, because they are stating this in the context of trademarks.
They are putting people on notice that they are guarding their signature brown color in the context in which they have a right, which is where that might lead to confusion with UPS's services - shipping boxes, delivery vans, private mailbox stores, etc. And they have some real exposure here.
First are the signature UPS vans, which also have signature fiberglass nose trim. They replace them by the thousands and sell the used ones. They are painted white before sale, but that is a cost they could escape if they could enforce their claim in the color. Also, the paint is very cheap, and the next owner will want to repaint them properly - brown might be a tempting choice.
Aside from selling to desperate (Amazon contractors who need trucks Right Now and can't wait in line for new ones) or small-fry (two guys and a truck) type delivery services, former UPS vans are wildly popular for those building a Tiny House onboard, aka #VanLife. This is increasingly popular due to pressures in the housing market - a Google employee even famously did it. However, people with houses do not like it. UPS does not want people looking askance at brown vans in their community, so they do not want to be associated with #VanLife.
Another area of vulnerability is that The UPS Store is franchised. Family-owned franchise operators are made restless by decisions made by UPS Corporate - ask any of them how they feel about Amazon returns "business". As such you have defections, and UPS wants to deter this by forcing "apostates" to spend money updating signs, trim and furniture to not be brown.
They could make all these claims without the disclaimer you note, but the disclaimer makes it easier to convince a jury that the actor reasonably should have known they were infringing.