Vivek Wadhwa has the better perspective on the matter. The author is assuming that "because people who believe in homeopathy are believing in something that does not follow from our scientific models, homeopathy must not work." But this is fallacious.
We all know about the placebo effect. Do we know the efficacy of homeopathy in the realm of the placebo effect? Perhaps a pill with a bogus (but plausible to the naive) reason has more power than a sugarpill with no explanation at all as to why it works. If so, by some definitions of efficacy (say, "works better than a sugarpill"), you would have to conclude that homeopathy works (albiet in the context of our world, where many are scientifically illiterate).
The universe does not follow our scientific model. Rather, it is always(1) the model that follows the universe. There will always(2) be inexplicable (and apparently scientifically impossible) phenomena, and the purpose of science is to find them.
(and also to simplify the axioms. Wolfram might be disappointed with the LHC outcome, but I'm hopeful that somebody will find a new model -- equivalent to the standard model, or at least one that leads to the standard model in other scales of physics -- that I can actually understand ;) )
(1) Well, never say neither always nor never, and mileage may vary based on unexpected factors.
(2) This I've concluded from Goedel's Incompleteness Theorem, but then again I don't actually buy that 100% either. I don't buy that (X implies X) implies (X is true), which I think is assumed in GIT. Input appreciated.
Now, this doesn't mean its real (or fake), it just means we need more research. Its also worth noting that the trials of homeopathy in the Shang 2006 article were rated as higher quality than those of conventional treatment (but there were less of them).
(or I read the wrong paper...)