My hunch is that this is no more true of C-levels than it is of any other profession where some natural aptitude (eg. above average intelligence) is required. In other words, I think the "pool" of C-levels is small almost solely because of organisational hierarchy; for every C-level there are many more people with the required natural aptitude who are not C-levels. Of course, for a sufficiently narrow domain, the intersection of people with the required natural aptitude and people with the required years of domain experience may become very small.
In that sense, I think being a C-level is something that many people can just "train up to," if given the right opportunities. I'm not sure if there is any empirical evidence that could tell us who's right.
I've seen enough "emergency temporary promotions" succeed in their job that I tend to agree with you and not with the self-serving "I am special" arguments you hear from people in these circles.