Does the principle of אלו ואלו דברי אלקים חיים apply in a historical מחלוקת about what happened? For example, whether the תורה was originally given in כתב אשורית or כתב עברי? Or when two אמוראים argue about what the תנא said?
It would seem that the rule of אלו ואלו דבדרי אלקים חיים would apply to debates pertaining to clarifying a question of halacha. The fact that the practical halacha sides with one view does not detract from the inherent truth in the opposing view. This is as we find in Eiruvin 13b that with regards to a machlokes Beis Hillel and Beis Shammai we are told the rule of אלו ואלו, and yet the Gemara concludes והלכה כבית הלל.
With regards to a dispute over a historical factual event it would seem that this rule should not apply. In truth however, we find the opposite is true. The Gemara in Gittin 6b brings a machlokes as to what was the catalyst which caused the tragedy of פילגש בגבעה, whether it was a fly or a hair which angered the husband. The Gemara concludes that on this machlokes as well we apply the rule of אלו ואלו.
One could argue that over there the Gemara concludes that in fact both were present the fly and the hair. In other disputes where such an answer is not feasible, such a the shape of the קרשי המשכן or whether קדש לה’ was written in one line or two on the ציץ, certainly we can’t apply this rule. Yet even here we find it is applicable. The Gemara in Shabbos 63b which records the above machlokes about the Tzitz, relates how Rebbi Eliezer saw the Tzitz with his own eyes in Rome and it was written on 1 line. The halacha however, still follows the Chachamim that it should be on 2 lines! Michtav M’Eliyahu [ח”ד 56-57] explains that once the clear tradition was lost the Torah is left to Chazal to interpret with their Ruach Hakodesh and Mesores. Any opinion they express has basis and truth in the Torah, and if according to כללי הוראה, the halacha follows one opinion, this outweighs even the historical facts. Tosfos Rabbeinu Peretz [Eiruvin 13b] explains further that the machlokes is that even if it historically was one way, this opinion holds it should have been the other way.
The Gemara in Rosh Hashana records a well known machlokes whether the world was created in Tishrei or Nissan. Here too the meforshim say we can apply אלו ואלו and that each one is referring to a different aspect of creation.
So while the historical facts where certainly one way or another we find that we can still apply the principle of אלו ואלו דברי אלקים חיים. As to the technical issue of what was said by which Tanna, it would seem the rule of Eilu V’Eilu would not apply.