ApJ: The paper uniquely connects magnetic fields threading the chromosphere to the overlying corona and other heated plasmas. No correlations were found between heated plasma and properties of chromospheric magnetic fields on scales below supergranules. Processes hidden from our observations control plasma heating. While improved magnetic measurements are needed, these data indicate that the corona is a self-regulating forced system. Heating depends on the state of the corona, not simply on boundary conditions. Heating models based upon identifiable bipolar fields, including cool loops, tectonics and observable magnetic reconnection, are refuted for these regions with unipolar chromospheric magnetic fields.