The finding of reduced functional MRI (fMRI) activity in the default mode network (DMN) during externally focused cognitive control has been highly influential to our understanding of human brain function. However, these negative fMRI responses, measured as relative decreases in the blood-oxygenation-level-dependent (BOLD) response between rest and task, have also prompted major questions of interpretation. Using hybrid functional positron emission tomography (PET)-MRI, this study shows that task-positive and -negative BOLD responses do not reflect antagonistic patterns of synaptic metabolism. Task-positive BOLD responses in attention and control networks were accompanied by concomitant increases in glucose metabolism during cognitive control, but metabolism in widespread DMN remained high during rest and task despite negative BOLD responses. Dissociations between glucose metabolism and the BOLD response specific to the DMN reveal functional heterogeneity in this network and demonstrate that negative BOLD responses during cognitive control should not be interpreted to reflect relative increases in metabolic activity during rest. Rather, neurovascular coupling underlying BOLD response patterns during rest and task in DMN appears fundamentally different from BOLD responses in other association networks during cognitive control.