We reconsider the bounds on non-standard neutrino interactions with matter which can be derived by constraining the four-charged-lepton operators induced at the loop level. We find that these bounds are model dependent. Naturalness arguments can lead to much stronger constraints than those presented in previous studies, while no completely model-independent bounds can be derived. We will illustrate how large loop-contributions to four-charged-lepton operators are induced within a particular model that realizes gauge invariant non-standard interactions and discuss conditions to avoid these bounds. These considerations mainly affect the Script O (10− 4) constraint on the non-standard coupling strength ε eμ, which is lost. The only model-independent constraints that can be derived are Script O (10− 1). However, significant cancellations are required in order to saturate this bound.