The Dicor two step process if done properly will bond. One of the steps is a bonding agent.
First make sure the black specks aren't just dirt that is really stuck on to the rubber. I would wash off my roof every couple of years and was always sure the white was going away. But once I used a soft bristle brush and scrubbed it turned out to be dirt. Once finished with the good scrubbing the roof looked like new.
My roof is 20 years old and has sat out in direct Southern California sun everyday since new. Last year I paid to have the 2 step process for my roof by an RV detailing company that works in the RV Resort we stay at during the summer. It was a lot cheaper than $1800. It took two people about 4 hours total. So far it's not peeling off.