If you are intersted, then it's worth the trouble to read through both of these threads.
The problem with trying to prove ancient Americans did indeed cross the Atlantic by following the Gulf Stream is that we don't know how the Gulf Stream circled the nothern Atlantic many thousands of years ago, and certainly not right after the end of the last ice age (well, not that I know of, anyway).
But to me it seems far more likely that - if it ever happend - it may have been the Inuit or those that lived in Greenland and north east Canada before them.
The chances some vessel/raft/boat from the Caribbean (or Florida) ended up in Europe seems less because of the much larger chance they drifted further south while travelling along the Gulf Stream, and would turn south and back west, back to the Americas (and probably be long dead by then).
I think I found a site which describes how the Gulf Stream looked during the last ice age:
From The Last Ice Age to The Present
During The Last Ice Age
Edited by Abramelin, 05 March 2010 - 04:31 PM.