Did Basques of the Ice Age travel to settle America?

Ice Age Columbus is a documentary fictionalizing certain theory: that the first settlers of the Americas didn't cross to the continent thru the Beringia connection (land bridge between Siberia and Alaska) but rather directly from Western Europe, following the edge of the ice shelf that covered the North Atlantic (without discounting the Beringian-Asian settlement, this just came afterwards). Some scientists defending this theory appear in the documentary, but it's mostly a recreation with actors (in the BBC they broadcasted it as Stone Age Columbus).

For me, as a Basque, is somehow thrilling (and chauvinistic, perhaps) to think about the idea... The Franco-Cantabrian refuge of the ice age in Western Europe was centered in this country of ours. The humans of the Solutrean carving culture depicted in the movie, painters of caves like Ekain, were living in this very countryside that is our home. And in the documentary, the adventurous tribe depicted gets out to the Atlantic from more or less the Basque Country (the northern tip of it, bordering the Landes region of France).

However, this idea has not many supporters, and the documentary does not check the counter-theories. It presents two things as if they were proven facts:

1. that Solutrean tools identical to the European ones appeared in Virginia (USA) 17,000 years ago (5 millennia before the arrival of other people from Siberia).

2. that traits of ancient European DNA are part of the Amerindian genetic inheritance (mixed with the Asian stock)

Yet, if you consult the Wikipedia, those two points are far from being accepted by the scientific community. Balancing what I have seen and read, it looks improbable to me, this idea of the Inuit-like Basques crossing the Atlantic 17,000 years ago. But it would have been fun and awesome if it were true, wouldn't it?