If you read on you'll see Dr. Caporale's explanation of this case. But in general synonymous sequences really are synonymous - there is no "hidden message" in most DNA and synonymous substitutions are quite common.
And it has no real relevance to common descent - after all the reproductive machinery which "understands" the "hidden meaning" is just as much a product of evolution and the same sequence might be nothing special in species which are not closely related.
Using the "same mutatiosn where synonymous ones would do" would help establish that the chimps are closer to humans than other apes. But it wouldn't be a major evidence for common descent on the grounds that synonymous mutations do tend to accumulate anyway - thats why the absence is significant. And they do that because these "hidden messages" are rare.
In fact the earliest studies (about 30 years ago) used proteins rather than genes and couldn't even detect synonymous mutations.