  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 $\mathcal O(10^{-4})$ constraint on the
non-standard coupling strength $\eps_{e\mu}$, which is lost. The only
model-independent constraints that can be derived are $\mathcal O(10^{-1})$.
However, significant cancellations are required in order to saturate this
bound.
