You had to look long and hard for asimplified tree of life to support your statement. If you had bothered to look for the adult version (linked from the same source as your diagram) you would get this:
http://tolweb.org/tree/phylogeny.html
I found this one that shows the complexity of birds and the mutation trace for them.
The other images I've found are far to large to post. This is the smallest I could find but it helps demonstrate the complexity.