I don't think it's twisted. The feral cats are non-native and introduced by humans (and in some cases propagated by humans). If humans act to un-do their previous acts, the results of which they find to be deleterious, aren't they just recognizing and rectifying previous mistakes?
Quite right.
You are absolutely correct. House cats, wether they are feral or tame, are non-native species. An example of eliminating non-native species is the elimination of Rainbow and Brown Trout in the Smokey Mountains National Park. Entire sections of streams have been poisoned to elinate the rainbows and browns so that the native Brook Trout can return.This is being done by the park service just in case you didn’t know. Non-native and invasive species have reeked havoc everywhere they are introduced. Examples, Cane Toads and feral cats in Australia, Brown tree snake in the pacific islands, Snake head fish in America. There are literally thousands of examples of non-natives destroying and replacing native wildlife. No mercy for non-native and invasive species.