Mom didn't just go to the police, she held a press conference in which she said that this should be treated as a hate crime.

If the kid were 16 I'd say, sure, kid probably made it up by herself. 11? Making up an extremely detailed story like this and sticking to it this long is, I think, beyond the ability of most 11-year-olds. Maybe she started telling the lie and her mom was so concerned/outraged that she just kept going because, as kids do, she was afraid that telling the truth would get her in more trouble and she wasn't really thinking through the long-term consequences. That would not be my first guess. 11-year-old is able to make this up and happens to have the kind of very specific parent who would try to make this a national incident seems like not the most likely explanation to me.