One would think when you rent a car, part of the rent is insurance
Liability insurance is included, collision damage insurance is at an additional charge. Sometimes full collision is half as much as the rent itself. There is still a deductible involved, unless you buy Island Car's "zero liability" coverage which costs $30 a day on top of the rental fee: http://www.islandcarrentals.com/Home.aspx/AutoCoverage

Insurance works the same way with rental cars in the US - CDW is around $10-25 a day, but many credit cards include that insurance if you use their card to rent - not so in Jamaica with 99.9% of credit cards. Very few will cover collision in Jamaica (or Ireland or Israel or Iceland, for some reason).