The aim of this paper is to revisit critically the current census of AGN as derived from optical spectroscopy. We considered the spectra of nearby (z<0.1) galaxies from the Sloan Digital Sky Survey (SDSS). The equivalent width (EW) distribution of the [O III]5007 emission line is strongly clustered around ~0.6 A, extending the validity of the results we obtained for red giant ellipticals. The close connection between emission lines and stellar continuum points to stellar processes as the most likely source of the bulk of the ionizing photons in these galaxies although their emission line ratios are similar to those of active nuclei. Genuine AGN might be sought mainly among the minority (~5-10%) of outliers, i.e., galaxies with EW>~2 A. The galaxies located in the AGN region of the spectroscopic diagnostic diagrams outnumber outliers by a factor 5-10 which casts doubts on the accuracy of the current identification of active galaxies, particularly those of LINERs of low line luminosity, <~ 10^39-10^40 erg/s. This conclusion can be tested by using spectra that covers smaller physical regions such as those that are already available in the literature of the ~500 nearest bright galaxies, with a stellar continuum reduced by a factor of 20-100 with respect to SDSS galaxies. If the emission lines were mainly of AGN origin, their contrast against the continuum should be enhanced. Instead, their EW distribution is similar to that of the SDSS sample, with just an increase of the outlier fraction. We conclude that the number low-luminosity AGN is currently largely overestimated with a sample purity as low as ~10%. As a consequence the properties of low-luminosity AGN should be fundamentally revised.
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