Kodiaks are genetically close to polar bears, but diversified many thousands of years ago. I can't imagine that polar bears, the product of an evolutionary process some 400,000 years ago, might be driven into extinction in remote places such as Svalbard. The brown bear population in northern Norway has been drastically reduced by hunting in the last 150 years, and they don't have the capacity to swim any distance, certainly not 500 miles. I doubt that polar bears would disappear via hybridization in Greenland, as well, since brown bears couldn't cross the straits to get there.  The same would be true for places such as Wrangell Island, north of Siberia. The conclusions of this article are very unconvincing. 

A late friend shot a polar bear near his home in Atqasuk, 20 years ago, and that's 50 miles south of the Chukchi sea.