Let me quote Vine Deloria who wrote about a similar dilemma in a book called America in 1942:

The Bering Straits theory is tenaciously held by white scholars against the varied migration theories of the natives and is an example of the triumph of doctrine over facts. Excavating ancient fireplaces and campsites may be exciting, but there are no well-worn paths which clearly show migratory patterns from Asia to North America, and if there were such paths, there would be no indication anywhere which way the footprints were heading. We can be certain of only one thing: the Bering Strait theory is preferred by whites and consequently becomes accepted as scientific fact.

We can use this to see the collision of world views that can occur when different cultures exist in the same world. Traditional natives, as Deloria points out, believe in something different than archaeologists. The fact exists that archaeologists do have ample scientific evidence for a migration. There are not only archaeological "campsites" as Deloria calls them but also genetic and linguistic evidence to support a connection between Native Americans and Asians.