"The signature of G-d is truth" (Sanhedrin 64a). "Accept the truth from wherever it comes" (Rambam, Introduction to Avot). There are few values more important than that of truth. While Jewish law allows and encourages one to tell a white lie for the sake of peace (Yevamot 65b), such has its limits.
As the Talmud is, at its core, an oral tradition—with the words before us a summary of “classroom”” discussion—it is not surprising that debates will occur as to what the “teacher” actually said.