That’s arbitrary with no practical distinction in results. Let me illustrate.Easy to answer. Native = there without human intervention. The natural spread of species into new areas over generations means the species is native.
The wikipedia page on native species sums it up beautifully.
"In biogeography, a native species is indigenous to a given region or ecosystem if its presence in that region is the result of only local natural evolution (though often popularised as "with no human intervention") during history. The term is equivalent to the concept of indigenous or autochthonous species.
"A native species in a location is not necessarily also endemic to that location. Endemic species are exclusively found in a particular place. A native species may occur in areas other than the one under consideration. The terms endemic and native also do not imply that an organism necessarily first originated or evolved where it is currently found."
A flea species that has never been to North America rides the back of a wild wolf from Siberia to British Columbia across the Bering landbridge. The flea is now introduced into America.
The same flea rides a domestic dog being transported by a human from Siberia to British Columbia by boat.
The results are the same. The flea got here by being transported by something else. It didn’t matter if it was a human, a dog, a wolf, or a bear, doing the transporting.
Ancestral coyotes were once present in Florida prior to known human settlement. They went extinct. In the early and mid 1900s, humans brought captive coyotes into Florida to train fox hounds on. Some of those coyotes escaped and began breeding with the local red wolves and feral domestic dogs. Concurrent with that, coyotes spread across the Mississippi on their own and by the 1970s had come into west Florida. The half-coyotes and full coyotes started breeding and now we have a large population of classic coyotes that sometimes trend larger than other coyotes due to the wolf and domestic dog genes buried deep their backgrounds.
Are coyotes therefore “native” to Florida? Its complicated. And ultimately irrelevant. They just “are.” And therefore its up to man to decide whether we find them useful to be here or not. We can either let them grow wild like a weed, or we can control them (the equivalent of pruning a plant), or we can (theoretically) wipe them out. Depends on what we want.
There’s no magic law of the universe that says that if a plant or animal does something without human intervention, its ok, but if it does something with human intervention, its unnatural and therefore wrong.