This conclusion was largely based on an unorthodox phylogenetic treatment of cnidarian and bilaterian homeodomain sequences that employed Neighbor-net analysis. Neighbor-net analysis is based on the neighbor-joining method [77], but it is explicitly designed to investigate and visualize “complex evolutionary scenarios” that cannot be accurately modeled by a bifurcating phylogenetic tree, for example, scenarios involving reticulate evolution such as gene recombination, hybridization, and horizontal gene transfer [78], [79]. The authors do not explicitly justify their use of Neighbor-net analysis rather than more traditional methods that produce bifurcating trees. The Hox radiation is thought to have occurred via a bifurcating process that involved repeated rounds of gene duplication and divergence. In support of this, there are many well-supported nodes in published Hox phylogenies. The Neighbour-network diagram presented by Chourrout et al. can make it more difficult to visualize these well-supported nodes because it is a two dimensional projection of a three-dimensional graph. We suggest that Neighbour-net analysis would have been more appropriate as a supplement to rather than a replacement for a traditional tree-building algorithm.
http://plosone.org/article/info:doi/10.1371/journal.pone.0000153#article1.body1.sec3.sec1.p4

The phylogenetic analysis of Hox gene data using hylogenetic network methods is actually far from being "unorthodox". Indeed, the confusion comes from the belief that Neighbor-net analysis is restricted to the analyses of "complex scenarios that cannot be accurately modeled by a bifurcating phylogenetic tree". Quoting Bryant & Moulton (MBE 2004), NeighborNet analyses can be used when "The central problem with these data is the large number of sequences and the small number of sites." as it is exactly the case when analysing the 60 amino-acid long sequences from the HOX homeodomain. In this case, again quoting Bryant & Moulton (MBE 2004), "Sampling error leads to substantial homoplasy between the sequences, and the relative lack of information in the data means that there will be millions, perhaps billions, of optimal parsimony trees. This is an ideal situation for a network analysis, because we can deduce features from the data without restricting our attention to a single tree." That's exactly why phylogenetic network analyses have been performed in Chourrout et al. (Nature 2006). It cannot be expected to obtain a single and fully supported phylogenetic tree when analysing 60 amino-acid long sequences among organisms that likely diverged more than 500 million years ago. Unlike standard tree building methods, phylogenetic networks (NeigborNet and Consensus Networks) allow to adequately display this underlying uncertainty.