There are so many things that are implied in this paper, not explicitly said.
The mutation rate here detected seems to be the emergence of chain-terminating (CT) mutations, which truncate protein coding genes, usually just one gene in a bacterium or phage, which would be possible to observe from inspecting a plate to see which colonies die or survive.
This is only a specific kind of mutation, but Drake assumes that its frequency is related to the overall mutation rate. Which is probably fine. Mutations we infer from this work arise spontaneously from a similar mechanism in all organisms. This is just ionizing radiation for the most part. So at a first glance we still believe this. That there are no specific mechanisms for mutation. Since this is usually ionizing radiation we would expect that the rate would go up when there's more radiation around and it most certainly does.
There are lots of reasons that animals and humans would have a smaller rate. Drake is including in the paper the involvement of DNA repair mechanisms in the experiment as they are intrinsic to the survival of the yeast and bacterial cases and the phage may also enjoy the benefit thereof.
In some organisms there is a lot more DNA repair possible. So that would mitigate the mutation rate in some cases like Deinococcus radiodurans.
Metazoans and diploid organisms which undergo meiosis for sexual reproduction have other methods for reducing the number of mutations they pass on. Meiosis and recombination will allow the removal of many mutations by competition in gametes. Since there are two copies of each chromosome, mutations are constantly being competed against their unmutated versions as gametes. Then eukaryotes have their own repair enzymes and conditions. Then lastly recombining into diploids, they also show mutations less often.
For these reasons and others, the mutation rate being even across the genome does not mean that that the mutations accumulate evenly. Mutations still tend to accumulate in regions where positive selection is operational. Here is an excerpt from a recent genomic comparison of five strains of rice:
Despite strong purifying selective pressures on most Oryza genes, we documented a large number of positively selected genes, especially those genes involved in flower development, reproduction, and resistance-related processes. These diversifying genes are expected to have played key roles in adaptations to their ecological niches in Asia, South America, Africa and Australia.