  When constraining the primordial non-Gaussianity parameter f_NL with cosmic
microwave background anisotropy maps, the bias resulting from the covariance
between primordial non-Gaussianity and secondary non-Gaussianities to the
estimator of f_NL is generally assumed to be negligible. We show that this
assumption may not hold when attempting to measure the primordial
non-Gaussianity out to angular scales below a few tens arcminutes with an
experiment like Planck, especially if the primordial non-Gaussianity parameter
is around the minimum detectability level with f_NL between 5 and 10. In
future, it will be necessary to jointly estimate the combined primordial and
secondary contributions to the CMB bispectrum and establish f_NL by properly
accounting for the confusion from secondary non-Gaussianities.
