Well, it’s actually nearer than you think. The closest point between the mainland of the two continents are only 85km from Cape Dezhnev to Alaska. If you include the islands, it would be only 4km apart (from Big Diomede to Small Diomade) Not sure if it’s that tiring, but it’s certainly cold.
Perhaps he was with these guys?.... In 2013, a team of 65 swimmers from 17 countries performed a relay swim across the Bering Strait, the first such swim in history. They swam from Cape Dezhnev, Russia, to Cape Prince of Wales, United States (roughly 110 km). Source: Wikipedia