We can replace the assumption that $M^{n}$ is Einstein with just a bound on $|\nabla{\rm Ric}_{M^{n}}|$ to obtain the same result. In fact, if we only assume a bound on the Ricci curvature $|{\rm Ric}_{M^{n}}|$, then (1.7) holds with the regularity scale $r_{x}$ replaced by the harmonic radius $r_{h}$, see Definition 2.2. Note that estimates on the regularity scale are much stronger than corresponding $L^{q}$ estimates for the curvature given in (1.6).