No, the writer is not correct.
First, sharks are not a species; they are many species.
Second, sharks most certainly have changed over millions of years. They are very successful in their niche, and so ancient sharks are still very clearly sharks, so the basic body form we recognize as "shark" has been around for a long time; but it is not unchanging.
Third, I would expect there will be some minor differences in cytochrome C sequences within some species; but that this will be unusual. This is because the sequence is so highly conserved. To test this would require many sequences from a single species. I do not believe the writer has such data. Most species, however, will tend to have a single uniform cytochrome C sequence, because of the strong conservation.
Fourth, actually, I think there
is cytochrome C variation within sharks. As has been pointed out, your other reference was actually for COX (I missed that, oops!). I can't find a reference for several shark species and cytochrome C; but someone with a bit of time might like to trawl the databases and find out directly. There is certainly variation in cytochrome B; reported in
Protein evolution in different cellular environments: cytochrome b in sharks and mammals, by AP Martin and SR Palumbi, in Molecular Biology and Evolution, Vol 10, 873-891. (July 1993).
Cheers -- Sylas