This is not great advice - the only way I have heard it in English would be "quarter past 11" to mean 11:15. Most people would just say "eleven fifteen".
You were just wrong. They explicitly gave the understood options as 15 before or 15 after. These are the options everyone uses in English -- not 45 before or a quarter of the hour before. In English no one says quarter of 12 to mean 11:15. You just explained it completely different from the ways it is interpreted in English. I understand the logic and how it might come about. Maybe it's very common in German, but it is not used that way in English. If you referred to 11:15 in that way to a native English speaker you would be misinterpreted.