It's more complicated than that. It actually turns out that several mathematical analyses since the 80s have shown inclusive fitness theory and group selection theory to be mathematically equivalent*. In fact, both sides seem to readily acknowledge this fact, so the two groups' appear to be arguing over semantics (where does selection "really" occur?)
This argument over semantics is best illustrated by the following quote at the end of the supplementary information for the paper in the OP:
Finally, we propose that kin selection among social insects is an apparent phenomenon which arises only when you put the worker into the center of evolutionary analysis. Kin selectionists have argued that a worker who behaves altruistically by raising the offspring of another individual, requires an explanation other than natural selection, and this other explanation is kin selection. We argue, however, that there exists a more convenient coordinate system.
* There is, of course, ongoing debate about this, and whether one theory is more general than the other.
Okay so now what I'm getting is more like:
Some animals (esp. social insects) behave "altruistically," i.e. via raising others' offspring. Some people consider the explanation "an altruistic set of animals produces more offspring which inherit their altruism" sufficient, and some people require saying "animals that behave altruistically toward their kin produce more offspring etc." and calling it "inclusive fitness." People who think the first way point out that people who think the second way are ignoring phenomena l...
I originally titled this post "The Less Wrong wiki is wrong about group selection", because it seemed wildly overconfident about its assertion that group selection is nonsense. The wiki entry on "group selection" currently reads:
However, it appears that the real problem is not that the wiki is overconfident (that's a problem, but it's only a symptom of the next problem) but that the traditional dogma on the viability of group selection is wrong, or at least overconfident. I make this assertion after stumbling across a paper by Martin Nowak, Corina Tarnita, and E. O. Wilson titled "The evolution of eusociality", which appeared in Nature in August of this year. I found a PDF of this paper through Google scholar, click here. A blog entry discussing the paper can be found here (bias alert: it is written by a postdoc working in Martin Nowak's Evolutionary Dynamics program at Harvard).
Here's some quotes (bolding is mine):
...
Check out the paper for more details. Also look at the Supplementary Information if you have access to it. They perform an evolutionary game theoretic analysis, which I am still reading.
Apparently this theory is not that new. In this 2007 paper by David Sloan Wilson and E. O. Wilson, they argue (I'm just pasting the abstract):
From the other camp, this seems to be a fairly highly-cited paper from 2008. They concluded:
I know (as of yet) very little biology, so I leave the conclusion for readers to discuss. Does anyone have detailed knowledge of the issues here?