But the key point is UA was not operating rescue flights to DR.

However, we don't know where UA was operating rescue flights and it there was some agreement with the State Department or other airlines where airlines took on specific countries.

Regardless there seems to have been a communications issue although the OP has never really detailed their efforts to reach UA (seems they were unwilling to wait on the phone and only looked at online information) but UA probably could have done better reaching out -- likely the traditional rescue flight protocols were designed for needing to handle a few countries, not the entire world.