Surveys have revealed a class of object displaying both high X-ray luminosities (LX > 1042 erg s−1) and a lack of a discernible active galactic nucleus (AGN) in the optical band. If these sources are powered by star formation activity alone, they would be the most extreme X-ray luminosity star-forming galaxies known. We have investigated the mechanism driving the X-ray luminosities of such galaxies by studying the X-ray emission of three moderate redshift (z∼ 0.1) examples of this class, selected from a cross-correlation of the Sloan Digital Sky Survey Data Release 5 (SDSS-DR5) and XMM–Newton serendipitous survey (2XMMp-DR0) catalogues. X-ray spatial and long-term variability diagnostics of these sources suggest that they are compact X-ray emitters. This result is supported by the detection of rapid short-term variability in an observation of one of the sources. The X-ray spectra of all three sources are best fitted with a simple absorbed power-law model, thus betraying no significant signs of star formation. These results indicate that the X-ray emission is powered by AGN activity. But why do these sources not display optical AGN signatures? We show that the most likely explanation is that the optical AGN emission lines are being diluted by star formation signatures from within their host galaxies.