Stellar-mass primordial black holes (PBH) have been recently reconsidered as a dark matter (DM) candidate after the aLIGO discovery of several binary black hole (BH) mergers with masses of tens of M. Matter accretion on such massive objects leads to the emission of high-energy photons, capable of altering the ionization and thermal history of the universe. This, in turn, affects the statistical properties of the cosmic microwave background (CMB) anisotropies. Previous analyses have assumed spherical accretion. We argue that this approximation likely breaks down and that an accretion disk should form in the dark ages. Using the most up-to-date tools to compute the energy deposition in the medium, we derive constraints on the fraction of DM in PBH. Provided that disks form early on, even under conservative assumptions for accretion, these constraints exclude a monochromatic distribution of PBH with masses above ∼2 M as the dominant form of DM. The bound on the median PBH mass gets more stringent if a broad, log-normal mass function is considered. A deepened understanding of nonlinear clustering properties and BH accretion disk physics would permit an improved treatment and possibly lead to more stringent constraints.