Earlier quoted context omitted.
But almost nobody proves that programs they write on computers work either. When was the last time you proved a program correct?
You don't prove that it's "correct," as there is no such thing as a "correct" program. You prove that it works.
And there is such a thing as a correct implementation of an algorithm. Running it does not exactly prove things either, and it might not necessarily work on actual hardware, but it does show that the person understands at least part of the material.