There is much debate about the arrow time. (Related disciplines are thermodynamics, statistical physics, quantum mechanics, gravity, inflation, so it gets technical.)
That certainly explains why we never observe entropy running exactly backwards, but there are conceivable pathways that could result in entropy running backwards into a less entropic state. For instance, put two gasses of equal density into a container, where one gas is on top and one is on the bottom, separated by a sheet of glass. Remove the sheet of glass. The gasses mix. Now, entropy could run backwards for no known reason, and re-order the gasses, but in the other direction; the top gas now separated on the bottom, the bottom gas on the top.
This argument, while essentially correct IMHO, doesn't seem to cover the entire state space of what backwards-running entropy could do. But it's still an interesting argument.
Actually, statistical arguments explain why we don't observe (in macroscopic systems) entropy running backwards. Yes, the molecules could, through collisions, spontaneously re-order. But that is such an unlikely occurrence that it's probability of being observed (for a large number of molecules) is very near zero.
This paper, and my post in reply, is about a question deeper than that, namely, why doesn't time itself run backwards sometimes, in essence? (That elides over some things, which unfortunately including the essence of the question, but there isn't a snappy English formulation of the problem that I know of.) Nothing seems to stop it, except inasmuch as it never happens so something clearly is.
What you're talking about is a foundation to that argument, but the argument itself is beyond that. While the physicist in question has hopefully considered the point I make, he certainly knows about the statistical nature of entropy. However, while that is necessary knowledge, it is not sufficient to explain the other mysteries of entropy that this paper is about.
I understood what the article was saying, but it seems I didn't understand what you were saying. If I understand it now, you are saying that to prove his case he has to not only show that entropy can't directly decrease by, essentially, undoing the process and getting back to the original state, but he also has to show that entropy can't decrease by the system ending up in a state different from the first, but yet which is also of lower entropy? It seems to me that you are correct.
Also, there is no net gain of energy or information in the system when the gasses are reversed which if I understand it correctly would be the case if it was reversed entropy.
'Disorder' is probably a better way to think about it than energy and perhaps information (I'm weak on information theory; I know it has similar concepts though). So, if the gasses simply reversed places, there's no net gain in disorder.
But it's certainly proper to think about it in terms of microscopic, reversible processes that tend to result in the most statistically likely final states. The second law "could" be violated, it's just not very damn likely.
Here are some good papers, look them up at http://arxiv.org
Hollands and Wald. An Alternative to Inflation. arXiv (2002) vol. gr-qc
Wald. The Arrow of Time and the Initial Conditions of the Universe. arXiv (2005) vol. gr-qc
Kofman et al. Inflationary Theory and Alternative Cosmology. arXiv (2002) vol. hep-th
Carroll. Is Our Universe Natural?. arXiv (2005) vol. hep-th
Carroll and Chen. Spontaneous Inflation and the Origin of the Arrow of Time. arXiv (2004) vol. hep-th
Lebowitz. Boltzmann's Entropy and Time's Arrow. Physics Today (1993) pp. 1-7
Wallace. Gravity, Entropy, and Cosmology: In Search of Clarity. arXiv (2009) vol. cond-mat.stat-mech
Maccone. A quantum solution to the arrow-of-time dilemma. arXiv (2008) vol. quant-ph