ONLY formal rental companies (like Hertz, Budget, Alamo, etc) offer real insurance. Like in the US, insurance packages are OPTIONAL. IF you rented from such a company AND bought (paid for) total insurance (Liability AND collision), you should be pretty much worry free, even IF you were at fault.
As some already mentioned, SOME credit cards do offer some (limited) coverage in SOME regions. Good luck on sorting out how much they will pay, especially here where it can be difficult to find out the exact cost realistic cost of the repair. In anyway, unless you had above insurance deal with a formal company, YOU will leave money here and be left with trying to get some or all back from your Credit Card company.
Third and worse case scenario, you rented from some local "street" company, which usually don't even really OWN all or any of the vehicles the peddle to unsuspecting tourist. Mostly, they are independently owned by "associates" of such company and left to them for a limited amount of time in the hopes of making ends meet. They are most likely totally under insured, if at all, as the owner may actually be behind with payments. Usually, these companies will have you sign a contract which may more or less conspicuously contain an article about a HEFTY deductible you the renter would have to pay, in case of a loss or accident. USD 3000.oo is not unusual.
In case of anything more than minor, many of these "street" rental folks will not have a problem to try to get you for even more with the help of local law enforcement and even seek to prohibit you from leaving the country (immigration at the airport) or withhold your pass port.
If you have a minor to medium damage on a vehicle with such a "deal", you may be better advised to seek to repair the vehicle at your own cost BEFORE you show it for return.
Depending on where you would be, some here can direct you to a trustworthy shop (I can for Puerto Plata).
... J-D.