No, this is not true. What people are referring to are that in certain places, at certain times, a few species of reef fish are likely to be carriers of ciguatoxins which cause ciguatera poisoning. This can cause numbness, reversal of sensations, vomiting, and in the most extreme cases coma and death with the paralysis of the nervous system. There are frequently outbreaks of this among certain reefs in the Lesser Antilles and happens sporadically throughout the Caribbean and tropical Southern Atlantic regions. This is particularly true of reef predators such as barracuda and to a lesser extent grouper. The problem is that fish can be excellent eating one day and the following week they can be dangerous. Eating fish in April or May has nothing to do with it specifically, but ciguatera poisoning is more common during the hotter months since the microorganisms that produce this poison grow faster in the hotter months on the corals. I worked with fishermen in the DR and ate fish all year round and never became sick with ciguatera poisoning. I have become ill from poorly stored fish (not well refrigerated) after eating in a few restaurants in the past. It is interesting to note that the fisherman kill and dispose of all barracuda caught on the north coast around Puerto Plata to Punta Rucia, but in Samana I ate excellent barracuda in coconut milk.
If you want to play it safe eat only eat pelagic fish (migratory ocean fish) such as tuna, mackeral, dolphin (Mahi Mahi), wahoo, etc. It is also generally safe to eat lobster, langostinos, shrimp, conch, and squid. Ask around while down there and if people say the seafood at a certain restaurant is good and fresh, I suggest that would be the place to eat. Have a great trip.