Accurate spectroscopy of molecular hydrogen isotopologues is used for testing quantum electrodynamics and searching for physics beyond the standard model. Recent measurements of energies of rovibrational resonances in the ground electronic state have reached a level of uncertainty lower than the magnitude of the hyperfine splitting. The underlying hyperfine components of the resonance clearly perturb sub-Doppler saturation spectra. The extent to which hyperfine structure influences the Doppler-limited spectra is not fully understood, as there are two contradicting experimental works that show either a 350 kHz shift or lack of any deviation from the central frequency of the resonance in the HD molecule. Here, we address this problem theoretically. Using the spherical tensor approach, we prove that the barycenter of all hyperfine-resolved spectra corresponds to the unperturbed transition frequency (the first moment of the hyperfine-resolved spectra vanishes). This property is directly transferred to Doppler-limited spectra: we show that there is no detectable shift due to the hyperfine structure unless the ratio of the Doppler width to the root-mean-square hyperfine splitting is less than 50.