Update: "The unbroken chain of Mesorah"
Seems like the machlokes that happened in the comments to my post actually goes back to antiquity. According to Elizabeth Shanks Alexander in her essay The Orality of Rabbinic Writing, there were two major understandings of Oral Torah. The first is the idea of the "unbroken chain of transmission" which focused on the "verbatim" transmission of tradition from teacher to student. This is exemplified in the first Mishna of Pirkei Avot, as well as the story in B. Eruvin 54b which described an ingenious method that Moshe used to ensure accurate transmission whereby first he repeated the Oral Torah to Aaron, then to his sons, then to the Elders, and then to the nation. Then Aaron taught the Oral Torah to his sons, while Moshe listened, then to the Elders, then to the nation, then the sons taught the Torah in front of Moshe and Aaron, and so on.
A different view of Oral Torah can be seen in other sources. This view sees the Oral Torah as an "actualization of interpretive possibilities already embedded within the text of the Written Torah". This is demonstrated by the story of Moshe, Rabbi Akiva and the crownlets on the Torah in B. Menahot 29b. "The second set of source represents the orality of the Oral Torah in a manner quite different from the first set. Here, Oral and Written Torah differ not only in the medium of their revelation but also in their degrees of relative fixity and fluidity. Whereas the words of the Written Torah are fixed for eternity, the words of the Oral Torah are unfolded in an ongoing manner through the vigorous engagement of student and teacher with the foundational text of the Written Torah."