Kleinman writes:
There are a couple problems with using homology to determine relatedness. The first is if you only use the coding portion of the genome and ignore the non-coding portions (which control the coding portions), you can come to very incorrect conclusions. For example, crocodiles have a beta-keratin gene so some may jump to the conclusion that that crocodiles are somehow related to birds.
They are using phylogenetic signal to determine relatedness, not homology all by itself. You can use the coding regions of open reading frames, the promoters upstream of the reading frames, transposon sequences, ERVs, pseudogenes, or just any old random piece of DNA almost anywhere in the genome. For different sequences you would have to take saturation of mutations into account which is why functional DNA, both coding and non-coding, is often used. There is a certain point where neutrally evolving DNA can see two or more mutations at the same site, but this would only be counted as a single mutation when comparing those sequences. That's what we would call saturation.
The other point is that DNA sequences are independent of morphology. If you wanted to, you could completely change DNA sequences and still get nearly identical species. You could start by changing the anti-codons on tRNAs which would create very different DNA sequences for the same amino acid sequence. The vast majority of vertebrate genomes have no sequence specific function, and they could be drastically changed without impacting morphology. Many, many proteins have no impact on morphology, such as cytochrome c, which means they could differ drastically even in species that are nearly identical from a morphological standpoint.
So there is no reason other than common ancestry and evolution why phylogenies based on genetic sequences should match phylogenies based on morphology.