Neither of those programs you recommended are designed for non-engineers, @peterquill.
Here’s what MIT’s SDM program says is required of applicants:
It’s very possible that Ms. Reeves took some supplemental classes in between her undergrad degree and graduate degree, or had some other special circumstance we’re not aware of.
I can’t find anywhere the Stanford MSE webpage says that applicants need only “have completed a course in differential calculus of several variables before applying.” Here’s what it says: