2 braisos vs. 1 mishna (Eruvin 37a)

On 36b Rav said that our mishna is wrong because Ayo's braisa disagrees. The gemara asks why he prefers Ayo to our mishna and answers because he has another braisa that supports Ayo. It still seems like 2 braisos vs. 1 mishna. We say later in the gemara that in a case of 2 vs. 1 we'd prefer to change the 1 than the 2 but here it's a mishna on the other side so I would've thought that the Mishna should win. I saw that Rabbi Bechhofer discusses this.

Teshuvos Kol Mevaser (2:46) critiques the work of a Rabbi in Vienna who put out a new edition of the Tosefta to Bava Kamma.

In the Introduction, the author cites our Gemara as an example of a tendency that Rav had to give precedence to a Tosefta over a Mishnah — since that is evidently what Rav is doing here. The author also cited Yevamos 83a, where Rav seems to even give precedence to a "non-Tosefta" Baraisa over a Mishnah. [Were this to be true, perhaps it could be seen as an extension of the concept of Rav Tanna u'Palig — Rav had the status of a Tanna, and therefore was entitled to dispute them (see Eruvin 50b).]

Kol Mevaser, however, rejects both examples.

In the first place, the Baraisa in Yevamos is a Tosefta – in the second chapter of Tosefta Bikkurim).

Moreover, Ido's Baraisa here is not a Tosefta!

Rather, states Kol Mevaser, it is only when there are two Baraisos that contradict a Mishnah — as is the case in our Gemara (see Tosafos to Yoma 54b d.h. Mai Shnah who define this principle; see also there that it is uniquely Rav's, and that others do not necessarily agree) — or a case in which there is some unique reason to prefer the Baraisa (as is the case in Yevamos 83b) that Rav gives the Baraisa precedence.

After reading his post, it struck me that it makes some sense that Rav would be the one to give precedence to a braisa over a mishna because Rav was Rabbi Hiyya's nephew (see the bottom of Moed Kattan 20a) and he compiled many of the braisos. We know that Rav was also a talmid of Rebbe but he doesn't give the mishnayos absolute credence over the braisos because of his relationship with Rabbi Hiyya.