No, comparing the DNA trees is based on silent mutations. These reveal the mutation rates, because they're not getting filtered out by selection.
Let's say one species mutates 10 times faster than the other. Doesn't that mean that it has 10 times the chance to get a NON-SILENT gene change? In other words, measuring silent mutations doesn't measure the etheral "helpful mutation" rate per se, but a species with a higher silent rate will, as I understand the theory, also have a better chance of more "helpful mutations".
Chimps and especially people have a very low mutation rate. So low that even the minor gene differences we see appear to be a lot of change in a little time. I understand a helpful mutation, if it happens, would be selected for, but if genes don't mutate much then a helpful mutation is indeed a rare unicorn. It does not matter that it will be selected for once it arrives, if it rarely arrives then I don't see how you get from A to B in the time allowed.