By that definition, horses that were introduced to North America by humans in 16th century are not invasive because they existed in North America 10,000 years ago.

The article also does say that Grizzlies come and go, that the significance here is it’s a female with cubs. So it’s not like grizzlies aren’t present at all on the island.

Of course there could be a boom but apex predators tend to not be super boomy since they’d outstrip their own resources first.

So they fill a niche in a place that evolved with extinct horses and can sustain another species of horse. If they pass a threshold where they drink all the water for example (desert pools on Australia with endemic desert fishes), they became invasive and must go.