Many drivers in Jamaica (or almost any country for that matter) carry the minimum coverage required by law. That is normally what is called "third party" coverage, which covers damages to others that the driver and vehicle may cause. But this does not cover the vehicle nor anything or anyone in the vehicle which caused the damages.
Paying passengers in a white plated vehicle are essentially breaking the law and no coverage would exist at all and you would be held accountable for damages done to others just as the driver would be.
As for an establishment procuring a ride for you, there is no minimum purchase requirement. If an employee of the business gets you a ride, the business now assumes the risk and their liability insurance will kick in. If you are unsure if a business has proper business insurance, then always ask them to get you a legal red plated taxi when asking for the ride. I would do this all time anyway.