Summary
Harry did not just receive a letter from Hogwarts, he also received a letter from the Mage's Association, Clock Tower Branch. Unlike Hogwarts that wasn't that...elaborative, the Mage's Association is...and its signed by someone named Kischur Zelretch Schweinorg. And his letter is more convincing than Hogwarts. So he signed up his name, and ran off to do his thing. To Clock Tower!