Kehilas Prozdor cites the MaHarik (12) who explores the possibility that R' Chiya eventually became a disciple-colleague to Rebbi, which might permit it. However, the Gemara (Bava Basra 158b) derives that Ben Azzai was a disciple-colleague to R' Akiva from Ben Azzai's use of the word "you" rather than "Rebbi", when addressing R' Akiva. Yet, the Gemara (Kidushin 49b) states that if a man betroths a woman on condition that he is a Chochom, he needn't be a Chochom like R' Akiva to fulfill the condition; if he betroths her on condition that he is a Talmid Chochom, then he needn't be like Ben Azzai to fulfill the condition. Thus, we see that Ben Azzai was still held to be a disciple of R' Akiva, despite being labeled as a disciple-colleague.
Therefore, the MaHarik concludes that it is permitted for a student to disagree with his teacher in matters of prohibitions (as R' Chiya did). However, the Gemara (Sanhedrin 110a) which characterizes one who challenges, quarrels or complains about his Rebbi to be as one who had done so to the Shechinah, refers exclusively to one's primary teacher (who taught him most of his knowledge) and non-prohibition matters. This is derived from the fact that Korach's group quarreled with Moshe, indisputably the primary teacher of Bnei Yisroel, but were characterized as contenders against Hashem.