There is one small problem with the end of the second clip. Even after Beringia flooded contact was maintained with the old world through sea travel. In short, people kayaked and boated from Asia to America, and are still doing it today.
The New World never lost contact with the Old World, all Columbus did was broaden that contact beyond what it had been before.
A slight problem would be they mention the "mitochondrial" Eve though considering they go into the switches from "Ts to Cs" I am guessing that in the omitted material that they don't explain genetic fixation and drift. They seem to give credence to the Garden of Eden mindset and otherwise compromises with a mythology. Yes, there was an ancestral Eve and an ancestral Adam and we can see that by tracing back the respective mitochondrial genome and Y chromosome. They just never met each other.