I tend to second this statement. The point is that although classical particles are in principle distinguishable due to their paths, we never know the starting point of these paths whose knowledge would correspond to a tremendous ammount of information entropy.Peters is saying that Gibbs' original paradox was based on inconsistent reasoning!
As you wrote, the assumption of "indistinguishability" makes no sense for classical particles. Yet it is thought to be necessary in Boltzmann statistical mechanics, implying that the concept of classical particles is fundamentally flawed. As Peters shows, this is incorrect. The classical assumption that particles are distinguishable leads to the same 1/N! factor as the opposite assumption. Statistical mechanics for classical particles is internally consistent, with no need for any assumption beyond the uniform distribution of probability.