What ID proponents are encouraging in the greater scientific community is honesty about the fact that both design and ancestry can create genetic similarity.
The fact that known natural biological processes can produce non-tree-like patterns is problematic not for ID proponents but for proponents of common ancestry.
On Monday, I will look at the consistency of the phylogenetically informative sites for the Baum et al. (2016) paper. Spoiler alert: It looks like design.