Apparently you didn't read the article at the link. The Russians reported that they sailed out from Egvekinot, which makes for a distance of 300 miles.
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Evidently you haven't looked at a map, and haven't noticed that Egvekinot is a port on the Chukchi Peninsula, from which the boat could sail, follow the coast of the peninsula until near St. Lawrence Island, and then cross the remaining 35-50 miles in open waters. Looking at a map would also help you notice that the most direct route to St. Lawrence Island is along the Chukchi Peninsula coast, from which US planes and ships would have to stand out at least 12 miles. You also ignore the fact that Russian fishing and whaling boats would be sailing in those Russian territorial waters and nearby international waters, just going about their normal business. IOW, whether this boat was inside or outside of the territorial waters limit, they would have looked like just another fishing/whaling boat until they had turned toward St. Lawrence Island and had held that course for sometime. That this boat was not just an ordinary fishing boat would, at most, been apparent for 2-3 hours, if they accidentally happened to be observed immediately.