Final answer:
The dish named for John D. Rockefeller due to its richness is Oysters Rockefeller. Rocky Mountain oysters, however, are deep-fried animal testes, not related to the seafood dish. A hypothesis for oyster-related sickness could be that the oysters were contaminated.
Step-by-step explanation:
The oyster dish named for John D. Rockefeller because it was considered to be so rich is Oysters Rockefeller. The dish does not involve Rocky Mountain oysters, which are actually not oysters from the sea but the testes of male animals, such as bulls or sheep, that have been deep-fried. As for the hypothetical situation where a number of people became ill after eating oysters in a restaurant, a possible hypothesis could be that everyone who ate oysters got sick, suggesting that the oysters themselves may have been contaminated.