Trademark challenges are distinct from UDRP. If you are using the domain to compete in a way that infringes trademarks, that indeed is fair game for a federal suit. The settlement from that may indeed result in an order to turn over the domain. The UDRP arbitration is a distinct (not based on sane rule of law) procedure. This is largely important because the domain namespace is smaller than the trademark sphere. Corporate names may or may not be trademarks but overlap in domain space as well.
For example, Alphabet is what Google calls their parent company. BMW already had the trademark (though litigation gave potential use of the mark to Google in the US). BMW still operates Alphabet.com and uses the mark most places other than the US. Google being a global corporation, has probably well decided not to use Alphabet much even though they have the US rights to it.
Another example. I own the domain "sensor.com." I founded a company called Sensor Systems back in 1993 back before the internet was as ubiquitous as it is now. We had marks for our market space (computer software). Turns out there are a half a dozen other Sensor Systems out there around the world. Notably, there's one that makes GPS antennas in California (who uses sensorsantennas.com). We have an amicable arrangement to redirect people looking for the other company. We also had an image processing software product in the early days called Xcalibur (a name that I detested). We got a cease and desist letter from a company that made a document processing system called Excalibur. After some lawyer chit chat we ended up with a similar agreement. Amusingly be ended up being bought by the same company and then were spun out again. The only "restriction" in the breakup was they wanted us to stop using Xcalibur. Actually, we'd already stopped and as I hated the name to begin with, I made that great concession to the deal.
