I can see two things happening here. One is that a species cut down to a small area is vastly more susceptible to accidental extinction due to floods, hard winters, disease or whatever. Two is the fact that the first time ordinary dogs, cats, and rats get introduced into one of Darwin’s island paradises, many of the exotic creatures get wiped out.
Alright then, how old do you think the dinosaurs were? Or do you believe there were dinosaurs?
Yes, but there’s also pockets of unusual development in remote areas. The fact that cats can wipe out lizards on an island doesn’t mean the lizards didn’t evolve.
There’s always the problem of species destruction when a new, unchecked predator is introduced into an isolated area that hasn’t reached equilibrium. Feral cats will do a number on birds... until coyotes move in. The fact that an introduced species can wreak havoc doesn’t mean (in my book) that it is “globally” better adapted.
These are specific situations, not overall proofs, one way or the other.