What Gross means is that QCD is well defined in the ultraviolet, so that if you take a lattice version and send the lattice spacing to zero, there is no divergence in the coupling as you take the lattice spacing small. Instead, the coupling goes to zero as the inverse logarithm of the lattice spacing, so very slowly.
This doesn't mean that QCD perturbation theory doesn't have ultraviolet divergences, it has those like any other nonsupersymmetric unitary interacting field theory in 4d. These ultraviolet divergences though are not a sign of a problem with the theory, since the lattice definition works fine. This is in contrast to, say, QED, where the short lattice spacing limit requires the bare coupling to blow up, and it is likely that the theory blows up to infinite coupling at some small but finite distance. This is certainly what happens in the simplest interacting field theory, the quartically self-interacting scalar.
There is no proof that the limit of small lattice spacing gives a proper continuum limit for QCD, but the difficulties are of a stupid technical nature--- there is absolutely no doubt that it is true. The full proof will require a better handle on the best way to define continuum limits for statistical fluctuating fields within mathematics.