The feral and roaming cat enablers are like some politicians. They repeat their myths often enough and some gullible people begin to accept them.
Take the myth about if you euthanize a feral cat bird killing machine "another one just like it" will move in. I learned basic arithmetic in the first grade, and it seems to me that as you take away each feral cat you leave a vacuum in our ecosystem our natural birds and predators can retake and thrive in!
Can you picture this scenario? Three muggers are beating up a TNR colony manager. A policeman comes along and asks "Would you like me to arrest a couple of these guys?" "Oh no," comes the reply, "It would only create a vacuum and more would join in."