The part about the wool-carders in Genoa is just a story. By the time he was 18 years of age he was sailing on ships owned by Rene of Anjou, one of the King of France's cousins, and Isabella's Grandpa!
"They" knew who he was, even if you weren't supposed to. His wife was a niece of the King of Portugual as well, and you didn't climb to such heights in the High Middle-Ages without being born with a privilege or two.
My money's always been on Columbus (Colombo to the cognizenti, and knowing that "BO" is an old Welsh and Breton prefix for "Mc", we have some interesting possibilities here) being one of Rene's cousins, or possibly even a batard or thereabouts.
To get to the point, it's very likely that all the Scanderhoovians in the world are descended from half a dozen of Columbus' Breton cousins, so what's the big deal?~!
I read that Christopher Columbus may either be Italian, Spanish, Jewish, or Basque.