I use both Progreso Insurance and La Colonial Insurance for our two cars, and they have paid 4 claims without one problem over the past 6 years. I have had 4 accidents that I would call medium/serious (each of my claims for just my own damage was for between $35,000 and 50,000, and they paid every peso of the repair bills.)
And yes, in every single accident I have had, it was the other party that either ran a red light, or a stop sign into my path. I couldn't avoid them, so I hit them hard. They lost in every case.
As well, the body shop replaced the damaged parts on my car with new replacement branded parts, and the insurance companies went along with this, without questions.
On a 3 year old vehicle that is valued at about $325,000. I pay about RD$28,000 a year in premiums for full coverage. On an older vehicle for liability only, with limits of (I think) $400,000 and $800,000, I pay about RD$5000 a year.
One note, in the second accident, and every one following, i explicitly told the AMET who showed up, look, it's their fayult, they ran the red light and I hit them. MY INSURANCE will pay for MY DAMAGE, and THEIR INSURANCE can pay for THEIR damages.
The cops agreed, I filed a report, and the insurors paid. No problems followed any of the accidents, as if my insuror expects this type of scenario, and so they choose to pay and move on. And they haven't seemed to jack up MY rates, (as they would probably do in the US).
I have heard that Seguros Pepin, which seems to be many dominicanos insurance of choice, (and meets the minimum legal insurance requirements,)costs about RD$2000 a year for liability, and NEVER pays out. (but it does meet the legal requirements ). That is why the taxis jsut go to a nearby street corner, get it pounded out for $1000, don't repaint, and just keep moving too.