Do phylogenetic networks support Intelligent Design?

It is always interesting to see what the media make of scientific publications. Some time ago, several of us were involved in a paper in Trends in Genetics advocating the more widespread use of phylogenetic networks (Networks: expanding evolutionary thinking), which seemed mild enough. For example, the Idaho State University press release about the paper made it onto the Phys.Org news site reasonably accurately (Amending the Tree of Life).

However, the Intelligent Design site Evolution News and Views had a different take on things (Demolishing Darwin's Tree), reaching a series of conclusions that might surprise stun the authors of the original Trends in Genetics paper. You will need to read the ID commentary for yourself (and you should, if only for your own education), but the final set of conclusions will give you some of the flavour:

One can only welcome this paper's bold proposal to overturn entrenched dogma ... the "network" diagram seems conducive to ID research inasmuch as it calls into question universal common ancestry via natural selection (i.e., neo-Darwinism), and seeks to portray the evidence honestly ... It's too soon to tell if Darwin security forces will let this band of independent thinkers gather a following. If nothing else, it shows (notwithstanding the insistences of the National Center for Science Education) that insiders know about the fundamental controversies in evolutionary theory, and are calling for some of the same reforms that advocates of intelligent design do.

I am not sure that all of these conclusions are logically consistent with the words of the original paper.