First of all, your statement is meaningless. What exactly does it mean to "know math"?

Here's an alternative explanation: math students do lots of computations, and sometimes make mistakes which they would be able to identify immediately if someone told them "you made a mistake on this line".

Kind of like how all programmers occasionally drop a paren or a semicolon. Does that mean no programmers "know programming"? Of course not.

In fact, if you've never made a stupid mistake programming, odds are you're not a very good programmer because otherwise, you'd have done enough programming that one of these mistakes became inevitable.

The only difference is that most programming is simpler than university-level mathematics, so with a few decades of research we figured out how to use computers to prevent us from making a lot of mistakes without impeding our productivity too much.

For example, from the article:

"In fact, the great mathematician Leonhard Euler published a computation similar to this in a book in 1770, when the theory of complex numbers was still young."

So another way of wording your post: Euler doesn't know math.

Similarly, many of the examples (e.g. calculators) could be interpreted as students knowing too much math, and excepting their tools or others to know the same "math" they know.