No offence, Craig & NorthCoast...but where is this information coming from about the difference between "No" and "No, thanks"?
Someone made these same comments on Trip Advisor and I was stunned and embarrassed by them along with my Jamaican friends that read the same comment.

Here's a bit of what I posted in TA...
"I would stick to being polite by saying "No, thank you".
There's no reason not to be polite....Jamaica in under the British Commonwealth & the Queen's English is taught in schools...Jamaican's know manners.
Just for interest sake...you'll often hear the phrase.... "where's my manners" and correct themselves. A "no, thank you" is completely understood by Jamaicans."

And to add...the Jamaicans wanting to make a sale deal with tourists every day of every year they've been a higgler...to suggest that they don't know what "no, thanks" means after literally hearing it hundreds of thousands of times is completely absurd. Jamaicans may not always respond with "no, thanks" when declining an offer, but to insinuate they don't understand is insulting and this how my Jamaican friends felt.