Do performed optical tests disprove local realism?

In all the earlier performed optical experiments on the Einstein, Podolsky, and Rosen paradox additional assumptions have been introduced and inequalities stronger than Bell's original one have been deduced. It is stressed that these experimental results violate these stronger inequalities but are compatible with Bell's original inequality. Therefore the experiments in question cannot provide a conclusive proof of the violation of local realism in nature but probably only show that the additional assumptions are not true.