The term "native" can be a bit tricky. Horses are native to North America if you consider 12,000 years ago the time of purity of our fauna. So are mastodons. No matter what we do things change. The non-native species that sends me into a dream state is the earthworm. Yep, there have been no native earthworms in the northern forests since the advance of the glaciers many thousands of years ago. There's evidence that there is a return, and the leading edge of that change is about here, in the middle of New England. The gardeners' friend and fish bait types probably originated in another part of the world, but there's a slow incursion of southern species moving north. When I'm digging around in the garden and turn up worms, I think about it for awhile. And I think about whoever studies and knows these things.
There's a discussion here