  One of the major open questions in the neutrino sector is the issue of
leptonic CP violation. Current global oscillation data shows a mild preference
for a large, potentially maximal value for the Dirac CP phase in the neutrino
mixing matrix. In this letter, we point out that New Physics in the form of
neutral-current like non-standard interactions with real couplings would likely
yield a similar conclusion even if CP in the neutrino sector were conserved.
Therefore, the claim for a discovery of leptonic CP violation will require a
robust ability to test New Physics scenarios.
