I'm no fan of the Kennedy clan but, from everything that I've read, this fact is pretty well-established. McMahon was very severely burned and unable to use his arms so JFK purportedly put one of the lifejacket straps between his teeth and towed the wounded engineer until they hit land.
I also remember that phrase from the song Jimmy Dean did about the incident:
McMahon, the Irishman, was burned so bad that he couldn't swim;
"Leave me here. Go on", he said, "'Cause, if you don't, you'll all be dead."
The PT skipper wouldn't leave him, a man to die alone at sea,
So, with a strap between his teeth, he towed the Irishman through the sea.