Your article is a little confusing. The Berin Strait theory does not suggest that all people's came from their respective continents except the Indigenous peoples of the Americas.
The idea is that our species, all of us, originated from Africa. From Africa, Homo sapiens expanded their range and slowly, over time, developed different superdicial characteristics, becomint different peoples, infiltrating all the different continents as they migrated.
Europeans came out of Africa. Middle Easterners came out of Africa. Asians and all the various Islanders came out of Africa. Australians came out of Africa. And all the various American peoples came out of Africa.
The Bering Strait theory says a massive migration of people crossed that area into the Americas during the last Ice Age from the other side, which is Asia major and when it happened. It was so long ago, it's inaccurate to say that Native Americans are decendants from Asians. It's more accurate to say that many Native Americans and modern day Asians share a common ancestor people who inhabited those lands 13,000 years ago.
The theory made sense, mostly in a geographical sense. But it was only ever a theory. It fell short in suggesting that the migrations only happened during that one time period and not considering sea travel.
I'm not sure how we get from that to this idea you're talking about that Indigenous Americans aren't a people in their own right, or are offshoots of some other people .... any more or less than anyone else.
Consider that there's evidence of humans in the British Isles from as long ago as 40,000 years, but only continuously for the last 12,000 years. So how could Americans have come from Europeans when they've been in America for longer than than people have been Britain?
People have been migrating all over the world all along, for more than 210,000K years.
There very well could have been a sizeable migration under thebcircumstances described by the Bering Strait theory. There probably was.
That doesn't negate the fact that somehow, some time, other peoples found their way to the Americas by other means from the old world, established themselves, and continued the process of migration, moving north. There's evidence.
You should know, however, that Clovis points, and the Clovis paleo-Indians genetically connect back to ancestral peoples of bortheast Asia. Clovis actually add weight to the Bering Strait theory.