Obviously, I was using the most extreme example to illustrate the point, but I was stunned to see that this figure isn't far off. According to some fairly recent data by Glazko et al., over 80% of the proteins of humans and chimps differ by at least one amino acid.
The paper also makes in the interesting point that "the estimate of 1–2% nucleotide difference is largely based on the comparison of non-protein-coding DNA, which has little effect on phenotypic characters. Therefore, for the general public who are interested in phenotypic differences, this is clearly misleading."
The paper is eminently readable to the interested layman - go here if you'd like to read it.