Left: distribution of the AGN fraction, with X-ray flux (black shaded area) and without X-ray flux (blue histogram). Right: distribution of the difference of the AGN fraction, with and without X-ray flux, for different luminosity bins. All distributions are normalised to unity. A tail appears at positive values, i.e., the AGN fractions are higher when X-ray flux is included in the SED fitting, for AGNs with L_X <  10⁴³ erg s⁻¹ that becomes more prominent for the most luminous sources (L_X <  10⁴⁵ erg s⁻¹). On the other hand, there is a tail at negative values, i.e. the AGN fractions are lower with X-ray flux, for the fainter AGNs (L_X <  10⁴³ erg s⁻¹, blue line).