Basically every person who writes papers using statistics has taken a course in statistics. Medical doctors do it, psychologists do it etc. And the statistics course you'd replace calculus with would be even lower level than that, basically worthless to everyone. At least calculus trains you to think about rate of change and slopes, statistics gives you nothing practical. It isn't like people remember those formulas so they can apply them in their daily lives.
People don't need to remember and apply formulas. They just need an intuition that they could be applied and how that might change the appearance of the statistics, as a kind of gauge of reliability. A tool for rationalization.
