Question about humans and monkeys both being unable to produce Vitamin C (due to the same genetic mutation) and creationism

Creationists, if I understand it correctly, claim that the genes for Vitamin C production got corrupt in monkeys and humans independently after the Fall of Man (whenever the Fall of Man might be: Young-Earth Creationists believe that was thousands of years ago, Old-Earth Creationists believe it was hundreds of thousands or perhaps millions of years ago). But there seems to be an easy way to prove that wrong: if that were true, we would expect there to be different mutations preventing the monkey's liver and the human's liver from producing Vitamin C. But, in reality, it's the same mutation in both monkeys and humans. So, what do creationists think, why is that reasoning faulty?