The Cubans' craft actually began to sink off the coast and they were rescued by a fishing boat, which took them close enough to swim to shore, the Palm Beach (Fla.) Post reported Monday.
The men turned up at the Ocean Club, where they were given T-shirts and towels and fed while a concierge notified Ocean Ridge police.
"I feel extremely proud to have made it here, and very, unbelievably thankful for the treatment I've received so far," Jose Alberto Gonzalez, 35, told the newspaper afterward, while sitting on a curb in the club parking lot.
Gonzalez, Raul Leiva, 46, and Nestor Cutino, 28, said through a translator that they left Puerto Padre Wednesday morning to come to America to live and work.
They may be able to seek U.S. residence under the federal "wet-foot, dry-foot" policy, in which Cuban refugees who make it to dry land can stay.
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