There has been an example in recent times of the elephant families ability to survive lengthy ocean swims. And as the descendent of the mammoths, this story helps reveals that it is not really all that mysterious that the mammoths were able to swim out to the Channel Islands.
Jerry Camarillo Dunn, Jr. learned in an interview with Tom Rockwell, the geologist who discovered the 95% complete mammoth skeleton on Santa Rosa in 1994, that a circus boat once sank off the Carolinas on the eastern American seaboard. The ship went down thirty miles from land. " The only animals that made it ashore were the elephants.
The elephants of today are surprisingly strong swimmers, a characteristic they seem to have inherited directly from their ancestors, the mammoths. They are even known to use their trunks like a snorkel to keep a fresh supply of air even when somewhat submerged !