Machloket of Gigantic Proportions

In Devarim 18:6-8 it is a described how a Levi can become a Cohen, if his soul desires. This of course is in total contrast to Parshat Korach, where the Cohanim must be descendants of Aharon. A Machloket within the early rabbinic Torah, as we have explained. In Bayit Sheni, they went according to Parshat Korach, and Devarim 18:6-8 was "explained" as Rashi "explains" it, following Sifrei 168. However, it seems from the way David chooses Zadok that he went according to Sefer Devarim. And so it was in Bayit Rishon. A Machloket of gigantic proportions.