This was largely just misrooting, coupled with ordinary long-branch attraction. Plus, it's old. (1998 is old for a molecular phylogeny.) -- The idea that kiwis are the sistergroup of emus + cassowaries is quite old, much older than molecular phylogenies, and has usually had widespread acceptance. The topology of Cooper et al. looks rather unsurprising, so, in the absence of a better analysis, I trust it.