From what I saw in recent figures, that isn't the case.
(And in reality, they do not possess the infrastructure to "flood" the market anyway. They can boost world production by about 1-3 percent if they went all-in, but I'd hardly call that a "flood".)
All oil prices are priced at the prices of those last few barrels sold that are in demand. Diesn’t take much production to have large effect. SA is only one capable of providing swing production.
Principle is like stock market. The many shares that are not traded are priced at the same value as the very few that are.