First, it's the Pet Monster 2 badge, not 11. (Perhaps it was just accidentally typing 11 instead of II).
Second, and to answer your question, if you look at recent winners, you can see that it gets awarded at 3:34AM/PM and 9:34AM/PM. Therefore, it is only given out at certain times, contrary to what it says in the requirements. (Perhaps that line needs to be deleted?)