Rosetta has detected the presence of the hydrogen halides HF, HCl, and HBr in the coma of comet 67P/Churyumov–Gerasimenko. These species are known to freeze out on icy grains in molecular clouds. Analysis of the abundances of HF and HCl as a function of cometocentric distance suggests that these hydrogen halides are released both from the nucleus surface and off dust particles in the inner coma. We present three lines of evidence. First, the abundances of HF and HCl relative to the overall neutral gas in the coma appear to increase with distance, indicating that a net source must be present; since there is no hint at any possible parent species with sufficient abundances that could explain the observed levels of HF or HCl, dust particles are the likely origin. Second, the amplitude of the daily modulation of the halide-to-water density due to the rotation and geometry of 67P's nucleus and the corresponding surface illumination is observed to progressively diminish with distance and comet dust activity; this can be understood from the range of dust particle speeds well below the neutral gas expansion speed, which tends to smooth the coma density profiles. Third, strong halogen abundance changes detected locally in the coma cannot be easily explained from composition changes at the surface, while they can be understood from differences in local gas production from the dust particles.