Many do. Like i said eaelier, my Cuban buddy talked about how.cigars with no rings/bands/labels are shipped by boat to the D.R. and banded as Dominicans.just gotta know which ones. I wasn't all that interested at the time sincenthe price was about the same ($30ish vs. $40ish for a cohiba or Monte Cristo...id rather have a Romeo y Julieta)
My favorite actually isn't Cuban, either; though those I've had were mostly delicious. Almost a buttery flavor, if such a word applies.
But this Fuente Chateau Natural is my new best ever cigar: 4.5x50, about $4 each online. Dominican Republic - burns slow, ridiculously smooth, tastes fantastic. First draw to the last.