Bell(δ) inequalities derived from separate common causal explanation of almost perfect EPR anticorrelations

It is a well known fact that a common common causal explanation of the EPR scenario which consists in providing a local, non-conspiratorial common common cause system for a set of EPR correlations is excluded by various Bell inequalities. But what if we replace the assumption of a common common cause system by the requirement that each correlation of the set has a local, non-conspiratorial separate common cause system? In the paper we show that this move does not yield a solution by providing a general recipe how to derive any Bell(δ) inequality---that is an inequality differing from some Bell inequality in a term of order of δ---from the assumption that an appropriate set of almost perfect anticorrelations has a separate common causal explanation