Definition of T’Ch may vary. Gemorah has a lot of discussions about T’Ch that go beyond just being “book smart” into middos and ability to recognize emes and do timely teshuva. And a classic apikoires Acher is not called T’Ch, I think, even as R Meir learns from him (the good part).
On the legit question on difference between RJBS and Saul Lieberman: R Moshe has a teshuva allowing to use Lieberman’s edition of Tosefta. He does not treat RJBS same way, he treated him as a chaver and a cousin. To what degree they were close? Relatives did not tell elderly RJBS that R Moshe passed away being afraid that this will affect his health, but he figured it out – as that yomtov was R Moshe’s turns to call him and when he did not, RJBS called himself and found out.
Unrelated, here is some interesting info I found on this topic
Saul Lieberman (son-in law of Meir Bar Ilan)was apparently drive by (1) desire for economic security that he could not obtain in other places (2) a hope to move JTS students towards more observance – his way of kiruv different, obviously, from the ways others looked at kiruv
When Agudat ha-Rabbanim publicly burned Kaplan’s prayer book in 1945, they wrote a public letter to ” “ha-Rav haGaon R. Shaul Lieberman, gavra raba ve-ish ha-eshkolot.” Quoting a secondary sourtce: The letter continues that they have heard that Lieberman treats Kaplan as one who has been excommunicated, but adds that this is not a solution. The letter concludes by stating that since they have so much respect for the learning and personality of Lieberman, they have therefore published this open letter. “We are concerned for his honor, which is the honor of the Torah.”
In a later discovered letter from Sail Lieberman, he responded: Lieberman expresses his pain that the open letter was published. He goes on to state that if the heads of Agudat ha-Rabbanim thought that it was forbidden for him to teach at the Seminary, why did they not summon him to appear before a beit din. Lieberman further states that before he accepted the job, he consulted with three universally recognized sages in Jerusalem. Although he does not reveal their names, he says that he is prepared to do so if necessary. only one of these sages refused to give a ruling. The second said that he did not see any clear prohibition against accepting the position at the Seminary. This is perhaps understandable; after all, there is no prohibition to teach non-Orthodox Jews. In accordance with this, R. Moses Feinstein ruled that as long as one is not pressured to teach anything in opposition to tradition, and especially if one needs the money, it is permitted to teach at a non-Orthodox Talmud Torah. The third sage said to Lieberman: You are the man, go and be successful, but only if you do not remain at the Seminary permanently … at the Seminary he is permitted to teach what he wishes. He also mentions that if another two or three Orthodox teachers joined the faculty, they could turn it into a wonderful place…and he would later successfully recruit a number of outstanding Orthodox scholars to join the faculty, either as permanent appointments or as visiting lecturers. Lieberman adds that since the Seminary officially recognizes the authority of the Shulhan Arukh, as long as this remains the case he hopes that much good will result from his presence there. “I say, with all due responsibility, that I am sure that my presence at the Seminary prevents the outbreak of a great dispute which would lead to a terrible hillul ha-shem.