It was fine for Elizabeth Taylor too, although she was friends with a few high profile Dominicans (and other Dominicans that are well known in the upper levels of society but otherwise unknown to the average Dominican.) The last time she visited the DR, a few years before dying, she finished her visiting Dominican friends trip with a few nights at the Casa Colonial hotel in Puerto Plata. Her visit was not captured by the international media or even the papparazzis, so I´m sure she truly got to enjoy her trip.
Many famous people visit the DR every year. Most visit without attracting too much attention or none at all. Dominican media tends to publish their visits after the high profile tourist left the country. That´s part of the appeal of a vacation in the DR. They can get away from it all.
I think it was last year that American rapper Jayc and Beyonce were spotted at a nightclub on avenida Venezuela. No mobs surrounded them, people weren´t lining up to take photos with them or get their autograph. People noticed them and for the most part respected their privacy and right to enjoy a night out among themselves. In other countries they wouldn´t be able to move an inch without fans interrupting them.