My response to the question posed below:
No, it does not obligate us to believe the statements are true in the literal sense. R' Yisroel Salanter states explicitly that incorrect statements are also Torah. Eilu va'eilu instructs us that the rejected position is also worthy of study and consideration.
What I meant was doesn't the concept of"eilu v'eilu" *obligate* us to believe thatall statements of Chazal are true? And if so,how then can one "choose" one statementover another in the case of a machlokesover a matter of opinion?