This is complete nonsense. The DR gov't is not going to deny entry to anyone arriving because of a previous overstay. They are generating revenue from the overstay fees, a lot of it.
Sneak out without paying your overstay tax - maybe. Try to renter after committing a crime in your home country, maybe. Passport flagged by USA customs and border patrol, maybe. Otherwise you'll breeze right through customs with nothing but a smile.
I suspect the money pulled in by exit fines by the small number of people that overstay(10's of thousands of people AT MOST) is dwarfed by the entry and exit fees now put into airline tickets by people who visit for a week or two (9 million or so people).
So the announcement by the Dominican Consulate in Canada is just nonsense and nothing will change?