However, in Eiruvin 13b, the bas qol is relied upon to give precedence to Beis Hillel. “These and those are the words of the living G-d, but the halachah is like BH.”
The two stories therefore appear to conflict on the question of the precedence of bas qol vs. normal halachic process.
1- Rav Nissim Gaon (Berachos 19a), opinion I: The bas qol said “halachah k’moso b’chol makom”. As a general rule, the halachah is like R’ Eliezer, but not here. The halachic conclusion does not contradict the bas qol, and it’s even possible that the BQ caused them to reach their decision.
2- Ibid, opinion II: The bas qol was only a test for the sages. Again, normally BQ would have halachic power.
3- Tosfos (Eiruvin 6b) I: The bas qol was only for the kavod of R’ Eliezer, who called down the opinion of Shamayim. BQ does NOT have halachic authority.
#3 is only possible (assuming that G-d doesn’t lie) by saying that R’ Eliezer and R’ Yehoshua were in an eilu va’eilu situation — both were right. Therefore, to show R’ Eliezer respect, G-d asserts that R Eliezer isn’t wrong even though the halachah is like R’ Yehoshua. In short, exactly the same point made by the BH vs BS story.
4- Tosfos II: There is a difference between whether the bas qol runs counter to metahalachah (normal halachic process), or in accordance with it. Bas qol can confirm a ruling, but not run counter to normal halachic process. Metahalachically, we follow BH because they are the majority. The BQ only confirms that fact.
(Why did it need confirmation? Probably because this is the first generation that the Sanhedrin was in exile, and because BS were generally considered the sharper group. Therefore there was a crisis in confidence in rejecting BS’s opinion without word from the Chamber of Hewn Wood.)
5- Or Samei’ach (Yesodei HaTorah 9:4): There is a distinction between whether the bas qol is clarifying a particular halachah and whether it speaks of a person’s ruling. In the first case, BQ is certainly not followed — metahalachah is the G-d-given means of creating new halachah. (cf
Temurah 16:1, where the prophet Yehoshua refuses to retrieve lost halachos via prophecy.) In the second, we do follow Beis Hillel, as per the BQ. (Although R’ Yehoshua disagreed about this use of bas qol as well.)
#5 appears to be nearly identical to #4, but with the added statement that given two true answers (speaking of one of two extant rulings), i.e. metahalachah allows one to follow either, BK can be followed. His conclusion is that even had BH and BS been of equal number, the halakhah would still be like BH.
In short, RNG gives authority to BQ to override halachic process, and the Achnai story’s bas qol is a special case for two different reasons. Tosafos and the OS agree that BQ has less authority than metahalachah, and possibly even no halachic say at all.
In either case it’s a question of whether one follows pre-existing rules for making halachic decisions despite supernatural evidence. It’s support for the notion of metahalachah, not for arbitrary leeway in making decisions.
FWIW, RYB Soloveitchik notes that “nitzchuni” does not mean “conquered”. Rather, by the normal rules of grammar it would be singular first person passive causitive of netzach (eternal). At the end of the Achnai story G-d is actually saying “My children have made Me [i.e. My Torah] eternal”. Which it would not be if we were limited to those decisions revealed at Sinai that weren’t lost.