The main purpose of this article is to elaborate on the limitations of using frequency-domain passivity theories in analyzing grid-inverter interactions within the low-frequency range. It primarily covers three levels of limitations: 1) the limitations and selection criteria of two kinds of passivity index, 2) potential conflicts between different passivity index tuning methods, and 3) the relationship between the frequency range of negative passivity index and system stability robustness. The findings suggest that caution should be exercised when applying passivity theory, particularly in the low-frequency range.