The article's point is perhaps that it's better to try and gain some intuition for whether or not you have the right answer, rather than checking the answer key. Relying on the answer key (or waiting for the teacher to say "you are right!") is an extremely poor habit and we should avoid teaching students to depend on that (in maths class or otherwise): in real life, there is no answer key.

One of the philosophical ideas of maths is that there are multiple ways of looking at a problem, and those multiple ways should feed back onto each other to confirm your answer.

Maths is not just a bunch of rules that have to be followed without question: in this case, maths is modelling something practical and the answer needs to match reality. Without that, the probability model could not even have been invented. If you can't get beyond the stage of do_question+check_answer, you are never going to be capable of anything more than grinding out other people's mathematical results.

I'm sorry you weren't taught maths by this person.