I have hear this about the Sa'ami (just to clarify, these are the Lapps in northern Finland, correct?) and their linguistic connection with East Asia and several tribes of Native Americans. Fascinating stuff, especially when one considers not only the post ice age migrations but what humanity may have looked like and what history was made in the preceding inter-glacial period when the climate was similar to what we've enjoyed for the past 10,000 or so years.
The Sa'ami linguistic connection had traditionally been thought to be "from the East", but that was back before DNA studies demonstrated that they were essentially THE ORIGINAL European population ~ now, the connection appears to be "to the East" where Sa'ami languages radiated from Fenno-Scandia to more primitive peoples to the East.
Currently, the Sapma, the area where the Sa'ami primarily live (exclusive of America where up to 90% of them currently reside) extends from Norway through Sweden, through Finland, and around the Kola Peninsula in Russia.
It is now known their range thousands of years ago was far more extensive.