In regular DMET, the bath orbitals (which exchange electrons with the impurity orbitals) are constructed from the Schmidt decomposition of the approximate mean-field wave function (which is computed for the full system). The resulting reduced-in-size "impurity+bath" cluster is then treated in wave-function theory as a closed system. Sekaran et al. have recently shown that this procedure is equivalent to a (much simpler) density matrix-functional Householder transformation when the density matrix is idempotent. They have also shown that, when the transformation is applied to a correlated density matrix, the cluster becomes an open subsystem. Therefore, if the full system is described at the noninteracting Kohn-Sham level (which is still exact density-wise), then the usual separation of the cluster from its environment is perfectly justified. The correlation potential then learns from the cluster (in which interactions are reintroduced, after applying the Householder transformation) through the density constraint.