I think the confounding notion here is that changes to the DNA which don’t affect a protein’s amino acid sequence are selectively neutral. It’s endemic, and yet there are several very obvious counterexamples. True. But as a first approximation, it is still a reasonable practice. For every 1000 amino acid changes one will find A LOT more functional effects than for every 1000 silent mutations. Keep in mind that your argument can be taken in reverse, too: there are some obvious examples where amino acid change does not result in a detectable change of properties.