The question is based on the perception that in Torah Shel Bal Peh we are trying to backwards engineer the Torah in order to figure out what Hashem's intention was. This approach leads to an understanding that when there is a Machlokes, one is right and one is wrong. Even when we say אלו ואלו — and take it to mean that both are somehow equally correct about the original intent — this will still leave the idea of נצחוני בני unexplained.
However, we find in Tana D'Bei Eliyahu Zuta 2 that the Torah Shebiksav is compared to wheat and flax-seeds that are given to us to embelish and make cakes and nice clothing therewith. By learning and expounding on the Torah, whilst being truthful to the rules of derivation, we are actually growing the Torah.
We can therefore find, אביתר בני כך הוא אומר יונתן בני כך הוא אומר and מאיר בני אומר, that Hashem will actually quote the Tanna about the Halachah. Hashem is quoting the author of the idea because it is actually this Chacham who brought this out. As the Torah Shel Bal Peh grows, the Torah becomes a growing and sprouting tree.
Now, while obviously Hashem knew all along what the Chacham will say, it is still the Torah brought about by this Chacham, and Hashem will wait until this person will bring out that Torah (or until He is ready to quote him).
It is for this reason that תורה לאו בשמים היא, that the Torah is not decided in Heaven. For we find that even when there is a discussion in heaven they will call upon earthly deciders to make the call. With this understanding, it becomes clear what is meant by אלו ואלו דברי אלקים חיים as well. If both sides apply equal intelligence and diligence, both perspectives can be equally valid, although we can only technically follow one ruling.
As for the actual concept of תורה לא בשמים היא, we find Tosafos in Bava Metzia, Pesachim & Chulin that we actually would pay attention to a heavenly call, but it was only in the case of Rebbe Eliezer that we ignored it since it was obvious that the voice was merely in his honor.