Let me try it this way....
Unfortunately, you (mrsDH) were unaware of the rules for duty free shopping. The rules are that you may buy duty free and carry it on the plane if this flight will be your final destination. You will have to pack it in your luggage if you have another flight to your final destination. It does not matter whether or not you are leaving a secured area or not, this is the rule/law! When we travel home from Aruba and go via the US, we clear customs in Aruba so no duty free as we will have to make a connection to our city in Canada. If we go Air Canada, we will have to clear customs in Toronto before heading off to our second flight. If we buy duty free then we must put it in our checked luggage (we will have our bags as we have to clear customs) or else we can not buy any duty free.
Chadd was not implying you were trying to break the law only but only stating that for those who have brought liquid duty free onto a second flight have done so by sneaking it through as it is against the rules. He works for an airline so he is the most knowlegable amongst us.
Unfortuately, it is not Jet Blue's fault in this incident as those are the rules set out by the TSA. Perhaps, the duty free shop in Aruba did not make themselves very clear or there was some sort of misunderstanding. Regardless, this was an unfortunate incident that was upsetting but the airline was not in the wrong.