You have to be realistic and plan accordingly. There is some top notch medical care to be had here. It's not available everywhere and just like at home some doctors are better than others. You just need to find (before hand) a hospital or clinic that is able to provide the competent treatment you expect for everyday maladies and injuries and ensure they accept the DR health insurance you have purchased. This place may not be exactly local to where you have chosen to live, or it could be. Think of it like moving to a new city with children, one of the criteria when choosing a place to live in the new place is proximity to a good school. Here proximity to good healthcare is a consideration.
If you break your arm, you should have no problem getting that treated here without a doctor suggesting that amputation is the best way to proceed. If however, you develop cancer, need a quadruple by-pass or treatment for another serious long term condition, having the option to return home to a first world environment might be advantageous and better in the long run.
Insurance here does have upper limits. A condition where treatment and convalescence takes place over a course of months, may result in someone reaching those insurance limits. Sometimes it is possible to travel home before treatment begins but not after. There are good oncologists here, and some not so good ones. There are great surgeons, and and some that are not so great.
The medical system here like the country as a whole is still developing. Continuing to live here with a serious chronic condition or developing one after you arrive could pose challenges. One has to consider how to deal with with medical problems that require urgent care when one cannot immediately find a doctor with the necessary skills or facilities to successfully treat you. Sometimes, timing is important. Farting around Santiago or Santo Domingo looking for the right specialist isn't always the best use of one's limited available time.
Those with preexisting medical conditions do not move to the third world without assessing the risk of doing so. Old people tend to need more medical care than younger people. Old people think about these things, young people probably not to the same extent. A heart attack in the US with available ambulance service is often fatal. Here with a less efficient ambulance service, more so. If you suffer from cardiac problems and move to the DR, you had better bring your own AED as you won't find one hanging on a wall here.