The same story "could" be told without ever mentioning the OR, like so: as soon as we have that formula_27 and formula_28 then we have that formula_29 Thus if, by random sampling, we manage to estimate formula_26 then, by rare disease assumption, that will be a good estimate of formula_31 which is all we need (besides formula_25 which we presumably already know by studying the few cases of the disease) to compute the RR. However, it is standard in the literature to explicitly report the OR and then claim that the RR is approximately equal to it.