Sure, but "cooking" is technological intervention, so the bar you are setting seems low to the point of being meaningless.
They may occasionally need certain vitamins that are rare in plants, but it's inaccurate to classify vegans as unable to satisfy their protein requirements. (And FWIW, there are natural vegetarian cultures that have survived without supplements.)
Vegetarians are fine, but vegans are at particular risk. I assume that's why op mentioned them to begin with.
They mentioned protein in particular, which isn't really that big of a deal (as opposed to certain other nutrients like Vitamin B-12, which can often be a problem).