Not true. Histones, the proteins that keep DNA ordered, are some of the earliest proteins. They provide an extremely accurate clock for when species diverged.
While on a short term, a few million years, you are right when you say the rate of genetic drift is not predictable. However, over a longer period of time the rate SEEMS to be fairly consistent. That is the point of the article.
You seem to be confusing genetic diversity with Phylogenetic diversity. Phylogenetic diversity describes how genes change physical differences while genetic diversity talks about the complexity of the genes themselves.
You can have genetic diversification without the physical structure of the organism changing, especially if there are environmental restrictions.