It says that it scrambles it "the same way" when it checks it. Isn't that clear enough? The scrambling is modulated by a random nonce which is stored together

It says that it scrambles it "the same way" when it checks it. Isn't that clear enough? The scrambling is modulated by a random nonce which is stored together with the hash. So you are scrambling the original randomly; you then scramble the password-to-be-checked the same "way" (ie. with the same nonce) to compare hashes.