Tosfos (Yevamos 14) asks how to square the Chachamim’s rejection of the bas kol siding with R’ Eliezer with gemara that tells us that a bas kol was accepted as proof that the halacha follows Beis Hillel and not Bais Shamai. Tosfos explains (in one of the two answers given) that the bas kol in favor of R’ Eliezer was rejected because it contradicted the majority view. The bas kol which supported Beis Hillel’s view was accepted because Hillel’s view was held by the majority. The only debate was whether the view of Shamai should perhaps be given more weight because Shamai was known to be sharper that Hillel.
Apparently, according to Tosfos, all things being equal, we do accept the evidence of a bas kol to establish halacha. It’s only in the context of having a rov that a bas kol is rejected. Contrast that with the Rambam’s statement in Hil Yesodei haTorah ch 9 with respect to a Navi:
או שאמר בדין מדיני תורה שה' ציווה לו שהדין כך הוא והלכה כדברי פלוני--הרי זה נביא שקר
According to the Rambam, it’s not just that a bas kol has no weight relative to rov – a bas kol is completely invalid as proof of what halacha should be.
The question raised in the previous post – why a bas kol outweighs the probabilistic evidence of rov with respect to whether a person touched a frog or sheretz, but does not outweigh the opinion of rov with respect to establishing halachic precedent – is valid only within Tosfos’ model that accepts at least theoretically, all things being equal, the evidence of a bas kol to determine halacha. However, according to the Rambam, the question is moot. Nevuah or bas kol is simply an unacceptable form of proof when it comes to psak.
What remains unclear according to the Rambam (which R’ Elchanan, who suggests this approach, and others struggle with) is why the bas kol which declared the halacha in accordance with Beis Hillel was accepted. Be that as it may, R’ Elchanan has a cute point with respect to the gemara’s statement that “Beis Shamai b’makom Beis Hillel aino mishna”, Beis Shamai’s view is unworthy of consideration. Why don't we find a similar sentiment recorded with respect to any other rejected view of Tanaim? Perhaps the reason is because no other Tannaitic view other than Shamai's was rejected by no less than a bas kol.