Don't see rooms mentioned in these statements. Spending any currency would enter their system in some manner (reported or underground). Spending US dollars probably does hurt somewhat the "reported" Jamaican Economy as they are often pocketed and not taxed as income."spending US dollars in Jamaica hurts the economy"... and "spending us dolllars in Jamaica will not enter their system"
I don't see the difference between buying rooms from a foreign owned entity or from a Jamaican owned entity entering the economy. Most room purchases are done pre-arrival in Jamaica and are recorded for taxation as soon as funds are received and accrued. These funds (though technically not yet realized as they are pre-arrival) are probably used to pay current liabilities like salaries and such.
Rooms that are purchased upon arrival may or may not be recorded and taxed regardless of currency. That is illegal, of course, but happens. The smaller property probably more frequently than larger places.