Seismic occurrence is characterized by clustering in space, time and magnitude. Correlations between magnitudes of subsequent events have been recently attributed to catalog incompleteness. Here we investigate the effect of catalog completeness on the amplitude of magnitude correlations. The analysis of two California regions with different levels of catalog accuracy and different lower magnitude thresholds indicate that the amplitude of correlations does not depend on catalog incompleteness. Conversely, correlations are controlled by the probability that two events belong to the same mainshock-aftershock sequence. Numerical simulations of the ETAS model, where magnitude correlations are absent by construction, provide a counter-test supporting our conclusions.