I once asked Putterman after a similar colloquium what he meant by this statement, and his answer was "long time tails". Long time tails are fractional powers that appear in the long time behavior of correlation functions, see, for example, here and here. These fractional powers are seen in molecular dynamics (they are more difficult to see experimentally), but they are not accounted for by the Navier-Stokes (NS) equation, and it is not completely obvious where these effects are hidden in the standard derivations of the NS equation from kinetic theory.
Long time tails are related to fluctuations, and so are ultimately a reflection of the fact that any coarse grained description must depend on a scale, and that the most general theory of non-equilibrium correlation functions at long distances and long times must involve more than a deterministic, continuous partial differential equation such as the Navier-Stokes equation.
The role of noise terms has been studied by a number of people, beginning with Landau and Lifschitz. The basic conclusions are:
1) There is a systematic low energy (long time) theory of correlation functions, which involves a gradient expansion of the conserved currents, and averaging over noise terms fixed by fluctuation-dissipation relations. The Navier-Stokes approximation corresponds to linear derivatives in the stress tensor, and no noise terms. This is a consistent approximation in three dimensions (but not in two).
2) At higher order noise terms have to be included, and kinetic coefficients become scale dependent. The hydrodynamic equations require a cutoff, and the best we can hope for is that low energy (long time) predictions are cutoff independent order by order in the low energy expansion.