I'm a New Yorker who makes frequent use of the yellow cabs here and has had the pleasure of using London cabs.
In NYC, it's basically the taxi's the are licensed. Any yellow cab has to have a
medallion and they are expensive... often going for $750k+ USD. Once you have the medallion you can lease/rent it to just about any hack who qualifies for a drivers license.
In London, it's the drivers that are heavily regulated. The tests are notoriously hard and London cabbies either have or acquire neurology that is much more spatially oriented than
normal.
The difference may be subtle to most people but it's important. When you get in a cab in NYC, you usually need to be explicit about the route that should be taken. Nefarious types will often take you through Times Square, Union Square, Canal Street or other traffic nightmares to run up the tab. London cabbies pride themselves (at least in my experience) on on knowing every last back road that will get you there that much faster.
So I see their point. They're a group of professionals.... who act like professionals. They've put a lot of time and effort into becoming such, I'd want to protect my turf as well.