Jefmaka,
If there is no family/blood relation and you are a tourist visiting the island, there would be virtually no incentive for anyone to let you borrow their car for anything less than an emergency. Considering the circumstances, it would be well within in the right of the insurance company to ask you to prove why there was no payment for use of someone's property. How could you prove that? And please remember that any barter arrangement would count as payment, so saying you brought stuff for them and they let you use the car would mean the car was hired out.
Insurance companies have lawyers working for them whose job is to find legal ways not to pay a fraudulent claim. What would you have on your side to contend this matter in court? And of course you would have to attend the court hearings at your own expense or a warrant for your arrest could be placed on you when you would return to the island.
So in simple terms, driving a car from anyone other than a legitimate rental company puts you and those in the car as well as the other drivers on the road at risk. So.... dont do it....