Resting-state functional magnetic resonance imaging (RS-FMRI) holds the promise of revealing brain functional connectivity without requiring specific tasks targeting particular brain systems. RS-FMRI is being used to find differences between populations even when a specific candidate target for traditional inferences is lacking. However, the problem with RS-FMRI is a lacking definition of what constitutes noise and signal. RS-FMRI is easy to acquire but is not easy to analyze or draw inferences from. In this commentary we discuss a problem that is still treated lightly despite its significant impact on RS-FMRI inferences; global signal regression (GSReg), the practice of projecting out signal averaged over the entire brain, can change resting-state correlations in ways that dramatically alter correlation patterns and hence conclusions about brain functional connectedness. Although Murphy et al. in 2009 demonstrated that GSReg negatively biases correlations, the approach remains in wide use. We revisit this issue to argue the problem that GSReg is more than negative bias or the interpretability of negative correlations. Its usage can fundamentally alter interregional correlations within a group, or their differences between groups. We used an illustrative model to clearly convey our objections and derived equations formalizing our conclusions. We hope this creates a clear context in which counterarguments can be made. We conclude that GSReg should not be used when studying RS-FMRI because GSReg biases correlations differently in different regions depending on the underlying true interregional correlation structure. GSReg can alter local and long-range correlations, potentially spreading underlying group differences to regions that may never have had any. Conclusions also apply to substitutions of GSReg for denoising with decompositions of signals aggregated over the network's regions to the extent they cannot separate signals of interest from noise. We touch on the need for careful accounting of nuisance parameters when making group comparisons of correlation maps.