The Charge of the Light Brigade?
Sounds like a lot of excellent old-style paleontological analysis. But, then there's this:
"Most gene-based studies suggest that arthropods and velvet worms are closely related to each other; however, our results indicate that arthropods are actually closer to water bears, or tardigrades, ..."
Their results use "cladistic analysis", which is basically creating a family tree by counting up matching features, then putting individuals with the most shared features closest together. The problem with this is, of course, that it's the human analyst who decides what's a feature and what's not. One analyst may count all hair on an organism as a single feature, while her compatriot counts scalp hair, facial hair, leg hair, nose hair, and ear hair(!) each as a separate feature. Since there's no objective *amount* of difference between features, the analysis is skewed by the choice of features.
The introduction of DNA analysis for use in creating evolutionary family trees has largely overcome this problem. Not only is DNA the actual genetic material specifying the creature's features, but one can often identify similarities between organisms' DNA that don't show in the physical animal (e.g. mutated genes that no longer can produce a gene product), or see that a feature that seems to be present in two animals is in fact encoded by unrelated genes in each, and thus is not an indicator of evolutionary relatedness (e.g. eyes that came about via completely different evolutionary routes).
Of course, if one compares only a tiny portion of the genomes of two animals (perhaps even just one or two genes), the chances of making an error in the evolutionary ordering are greatly increased. I hope that's the situation the paper's author is referring to here, rather than claiming to have overturned a robust DNA-based evolutionary tree.