What do you think I'd want to correct? That page says the same thing you've already been told twice: there is no underlying mathematics, and the meaning of the notation is defined by the notation. Here's a quote:

> These rules are meaningful only when the usual notation (called infix notation) is used. When functional or Polish notation are used for all operations, the order of operations results from the notation itself.

You could "correct" that to observe that "the order of operations results from the notation itself" is true of all notation, including infix notation, but why? It's not wrong now.

Can you really not tell the difference between "notation" and "math"?

"Order of operations" is the order in which operations proceed. Hence precedence.

They aren't a fact about mathematics. They're a fact about notation. Operator precedence and order of operations are synonymous.