Shared fusions between ancestral chromosomal linkage groups have previously been used to support phylogenetic groupings, notably sponges with cnidarians and bilaterians to the exclusion of ctenophores, rendering ctenophores the sister group to all other animals. The linkage groups used to identify these fusions were assessed for statistical significance relative to a model of randomly shuffled genes. I argue that the method of random shuffling treated all species as equally distant from each other, and so over-estimated the significance of the observed linkages. I calculate alternative statistics, and further argue that there are likely to be real linkage groups which are not identified as significant. If linkage groups are not supported statistically, they cannot reliably be used to identify shared derived chromosomal rearrangements, and hence phylogenetic hypotheses derived from them are suspect.