The finding of reduced activity in the default mode network (DMN) during externally focused cognitive control has been highly influential to our understanding of human brain function, but 'deactivations' have also prompted major questions of interpretation. Using hybrid functional PET-MR imaging, this study shows that fMRI task activations and deactivations do not reflect antagonistic patterns of synaptic metabolism. FMRI activations were accompanied by concomitant increases in metabolism during cognitive control, but, unlike the BOLD response, metabolism in the core DMN did not change between rest and task. Metabolic increases along the borders of the DMN during task performance further revealed a set of regions that guide engagement and suppression of neighboring networks during cognitive control. Collectively, dissociations between metabolism and BOLD signal specific to the DMN reveal functional heterogeneity in this network and demonstrate that BOLD deactivations during cognitive control should not be interpreted to reflect reduced synaptic activity.