  Motivated by a recent paper by the RBC-UKQCD Collaboration, which observes
large violations of the na\"ive factorization hypothesis in $K \to \pi \pi$
decays, we study in this paper the accuracy of the Vacuum Insertion
Approximation (VIA) for the matrix elements of the complete basis of four
fermion $\Delta F=2$ operators. We perform a comparison between the matrix
elements in QCD, evaluated on the lattice, and the VIA predictions. We also
investigate the dependence on the external meson masses by computing matrix
elements for $K$, $D_s$, $B_s$ and static mesons. In commonly used
renormalization schemes, we find large violations of the VIA in particular for
one of the two relevant Wick contractions in the kaon sector. These deviations,
however, decrease significantly as the meson mass increases and the VIA
predictions turn out to be rather well verified for B-meson matrix elements
and, even better, in the infinite mass limit.
