Dear Avira,
This topic is about controversies. Perek Shirah is largely considered to be a legitimate midrash that appeared somewhat suddenly. Which is normal and uncontroversial. However, there were instantly two claims that it was forged. One of the Rishonim said it was forged by a Karaite. And a notable Karaite claimed that it was a forgery from a mideastern rabbi. So the controversy is how can two opposing theologies, see a forgery in the same work.
Similarly, there is an old discussion if there used to be many different versions of the Sifre and Sifra. Or if the one we possess today is the one often mentioned in the gemara…. Etc… No malice intended. My apologies.