From what I've read, all the big name cigar companies/families started operations in the Dominican Republic, Honduras, and other Caribbean locations years ago, using their best Cuban seed. So their cigars from those places have rivalled the legendary old Havanas for years.
I've also read that the biggest source for cheap, shitty knockoffs of big-name Cuban Havanas is Havana itself. Just because a cigar is made in Havana, Cuba, and wears a famous name, doesn't mean it really came from that maker in Havana. Sure, the big names still make them there, but there's a lot of Back Alley Julios making them too.
So I've read and been told.
Just go to Edwards Tobacco in Englewood on Broadway, they'll hook you up.