"You know what they call people who graduated bottom of their class in medical school? Doctors."

Most people are clustered somewhere near the middle of the normal distribution in terms of the testable attributes supposedly required for highly specialized work. Most jobs that are just jobs (as opposed to Nobel laureates, astronauts, etc) have enough people in their number that they can't only contain truly exceptional outliers.

In other words, the only people who are outright excluded for such specialized jobs are negative outliers, who often have identifiable genetic/developmental problems or injuries. Everyone else at least has a shot, like you say.