We study dilepton production in proton-proton, Cu+Cu as well as in Au+Au collisions at the center-of-mass energy 200 GeV per participating nucleon pair within an extended statistical hadronization model. In extension to earlier studies we incorporate transport calculations for an estimate of uncorrelated e+e- -pairs from semileptonic D meson decays. While the invariant mass spectrum of dielectrons is well understood in the p+p collisions, severe discrepancies among different model scenarios based on hadronic degrees of freedom and recent data from the PHENIX Collaboration are found in heavy-ion collisions in the low mass region from 0.15 to 0.6 GeV as well as in the intermediate mass regime from 1.1 to 3 GeV when employing the standard dilepton sources. We investigate, furthermore, the background from correlated dileptons that are not emitted as a pair from a parent hadron but emerge from semileptonic decays of two correlated daughter hadrons. Our calculations suggest a sizeable contribution of such sources in central heavy-ion collisions in the low mass region. However, even the upper limits of our calculations are found to be far below the dilepton mass spectra of the PHENIX Collaboration.