I have read in many places that Parah could be a bliblical requirement to read.
Why is that? Zachor makes sense (as it says so in the Torah here). Why Parah?
The Beit Yosef in OC 685 quotes Tosfot who says that Parashiyot Zachor and Parah are Biblical requirements. However, our versions of Tosfot do not have anywhere that Parah is Biblical. The Mishna Berura OC 685 sk 15 writes that most Achronim agree that Parah is not a Biblical requirement. So we really don't know what source Tosfot had in mind (assuming the Beit Yosef's version didn't have a scribal error, which is possible).
The sifra derives from here that the ashes remain effective even nowadays without the Temple. However, later on the pasuk repeats (Numbers 19:21):
The Aruch HaShulchan posits that this extra occurrence of the phrase comes to teach that one should be involved even without the ashes by learning these verses which we do by reading them publicly once a year.
Again, this is all speculation because we don't have an original derivation (as I explained above).