[en] We argue that the asymptotic behavior of the weak matrix elements involving the on-mass-shell ground-state mesons with infinite momenta, which was instrumental in explaining the |ΔI| = 1/2 rule in the K → ππ decays, actually implies the vanishing of the matrix element of the local |ΔS| = 2 quark operator arising from the box diagram, when it is taken between |K⁰| and |K-bar⁰| states. In contrast, the long distance contribution, arising from the ππ intermediate states as well as the poles of the vector and pseudoscalar mesons, may alone reproduce the observed K_L-K_S mass difference, in consistency with the selection rule and the rates of the K → ππ decays, depending on the values of the η-η'- · mixing. (author)