Oh no, there's substantial variability among great mathematicians on this point. If I make this article into a top level point I should add qualification to this effect. I don't have the exact quote at hand (will add later), but for counterpoint I'll say that in the same book Don Zagier describes how when he was eleven his teacher told him that if he wanted to, he could read advanced math books in class provided that he precommitted to getting perfect scores on all of his exams. He said

She told me that I could choose whether or not I wanted to accept these conditions, and of course I did. It was very good training because I learned to be quick and careful even in routine calculations, and that was very helpful later.