There were “two different interpretive approaches were available to amoraim and stammaim who needed to disagree with the anonymous view of the Mishnah”

…we find that two different interpretive approaches were available to amoraim and stammaim who needed to disagree with the anonymous view of the Mishnah: to label the anonymous view as a minority opinion (bRH 16a and the sugyot cited by Sherira Gaon), or to expand the Mishnah to allow for multiple possible authors, including the one preferred by the redactors (the three sugyot analyzed above).  The first form assigns the anonymous view to a minority and thus rejects the Mishnah, while the latter form allows the Mishnah to follow multiple views, thus reconciling the halakha with the Mishnah, even though it does so at the expense of reinterpreting the Mishnah.

Richard Hidary, “The Agonistic Bavli: Greco-Roman Rhetoric in Sasanian Persia”, in Shoshannat Yaakov: Jewish and Iranian Studies in Honor of Yaakov Elman, ed. Shai Secunda & Steven Fine (Leiden & Boston: Brill, 2013), 162.