Frequently, when the Gemara tries to disprove Rav from a Mishna, it answers that he's considered a Tanna and can argue on a Mishna.
But there's this case in Berachos 37a, where Rav and Shmuel both say that one doesn't say a Mezonos on rice, and the Gemara concludes with a "תיובתא" (a conclusive refutation) against them.
Why doesn't the Gemara answer here that Rav is a Tanna?
I thought to answer as follows:
When the Gemara answers that Rav is a tanna, that is when the question is on Rav alone. In this case the question is on a joint statement of Rav and Shmuel. (Whether there is also a concept of "Shmuel is a tanna" as well is subject to debate, but for the sake of this answer let's assume that there isn't.) Thus even if the Gemara were to answer here that Rav is a tanna, it wouldn't help for Shmuel, who would still be refuted.
Now one could retort that if Shmuel is agreeing with Rav and Rav is a tanna then Shmuel should be on safe ground. However, in Ketubot 8a there is a statement that is cited first in the name of Rav and then in the name of R. Yochanan. When the Gemara challenges the statement of Rav it answers that Rav is a tanna, but when it challenges the statement of R. Yochanan it gives a different answer. Tosafot there asks why R. Yochanan couldn't defend himself by saying that he agrees with Rav who is a tanna. Tosafot answers that R. Yochanan frequently argues with Rav, which shows that even if Rav considers himself a tanna R. Yochanan does not consider Rav to be a tanna. If that is the case then R. Yochanan cannot now hide behind Rav, saying that he is a tanna.
ואין להקשות דאמאי לא משני רבי יוחנן אנא דאמרי כרב דתנא הוא דרבי יוחנן לא היה מחזיק רב כתנא דפליג עליו בכל דוכתא
Here, too, then, Shmuel would not be able to defend himself by saying that Rav is a tanna, because Shmuel frequently argues with Rav. Thus, in this case the concept of "Rav is a tanna" wouldn't help because Shmuel would still be refuted.
I subsequently found that R. Chizkiya Medini says that R. Yisrael Dushwitzky wrote to him giving this exact explanation to answer your question:
Sedei Chemed (entry for "Rav Tanna Hu U'Palig")
ועל זה כתב לי הרב המאוה"ג מוהר"ר ישראל דישאוויצקי מעיר מאהליב דינפער יצ"ו וזה לשונו במכתב לחזקיהו דף ט"ז ע"ד העיר כת"ר שליט"א בהא דברכות ל"ז א' דאמרינן תיובתא דרב ושמואל תיובתא האיך מסיק הש"ס בתיובתא ולא משנינן כבעלמא רב תנא הוא ופליג ולפי עניות דעתי פשוט דבודאי על רב לא הוה סלקינן בתיובתא דמצינן לשנויי רב תנא הוא ופליג רק בשביל שמואל סלקינן בתיובתא ולא הוה מצינן לשנויי ושמואל אמר לך אנא דאמרי כרב דתנא הוא דהא שמואל לא היה מחזיק את רב לתנא מדפליג עליה בכל דוכתא וחזון כזה נמצא ממש בתוספות כתובות ח' ע"א גבי ר' יוחנן והרבה הארכתי בכל זה בספרי חמדת ישראל עד כאן לשונו יצ"ו
There is another gemara where Rav is refuted from a beraita, and the gemara does not answer that Rav is a tanna who can argue.
Take a look at Menachot 5a (today's page in the Daf Yomi cycle!). Rav is of the opinion that an asham metzora (a leper's guilt offering) which has been slaughtered shelo lishmo (with the intent that it not be an asham metzora but something else) is not offered up.
מיתיבי אשם מצורע שנשחט שלא לשמו או שלא ניתן מדמו ע"ג בהונות ה"ז עולה לגבי מזבח וטעון נסכים וצריך אשם אחר להכשירו תיובתא דרב
The Gemara raises an objection from a baraita: With regard to the guilt offering of a leper that was slaughtered not for its own sake, or if none of its blood was placed on the leper’s right thumb and big toe, this guilt offering is offered up upon the altar and it requires libations, in accordance with the halakha of the guilt offering of a leper. But the leper must nevertheless bring another guilt offering to render him fit to partake of offerings. This baraita is a conclusive refutation of the statement of Rav, who said that the guilt offering of a leper that was slaughtered not for its own sake is entirely disqualified because it did not render the leper fit.
(Translation and elucidation from Sefaria)
Tosafot ad loc. picks up on the fact that the gemara could have explained that Rav is arguing in his capacity as a tanna, but chooses not to.
הוה מצי למימר רב תנא הוא ופליג כדקאמר בכמה דוכתי
It could have answered that Rav is a tanna who argues, as it does in other places.
Tosafot does not explain why the gemara did not in fact do so.
Unfortunately, Alex's fantastic answer won't help us in this case, as it is only Rav's opinion here which is at stake, not Rav and Shmuel together as in Berachot 37a (the focus of the question).
An explanation is offered by Yad Malachi 150 (basing himself on Kesef Mishneh to Hilchot Ma'asei HaKorbanot 5:6):
אי הוה שמיע ליה לרב ההיא ברייתא לא הוה פליג אתנא
Had Rav heard of that beraita he would not have argued on the tanna.
Thus, the gemara will only invoke the principle of רב תנא הוא ופליג, that Rav may argue on a tanna, when it knows that Rav was aware of the tanna's statement, and chose to argue regardless.
However, if Rav did not know of the opinion of the tanna, as is presumed to be the case here, then we say that Rav would presumably have backed down were he to have become aware of it. Thus, the tanna's statment is an effective refutation of Rav's position.
In that specific case of Berachot 37a, Chazal rejected the reasoning of Rav and Shmuel, so there was no need for the Gemara to support their statement by saying he/they were a Tana. This is in accordance with the rule of "going with the majority".
In the case where Rav is considered a Tana, it's because he can argue on another Tana since he was among the later Tanaim(last Tana, first Amora; he lived 400 years). However, Chazal can reject the ruling of any Tana or Amora(according to their times) should they see the emet being contrary to their ruling and the subsequent ruling would be binding on the disagreeing parties, as in the case of rice/mezonot mentioned above. So even if he/they are a Tana, Chazal rejected their reasoning in favor of their collective ruling.
Rav Elchonon Vasserman says in the name of Rav Chaim Soloveichik(Rav Yoshe Ber's grandfather) in Kovetz Shiurim on Bava Basra (# 633) that really an Amora could argue with a Tanna if he has the confidence to, but they simply wouldn't since they were so sure that whatever the Tanna says is correct, they would automatically rescind their opinion in face of the Tanna who was much greater than them. But since Rav was so old and in the time of the Tanaim (see Gittin 58b-59a, where Rav discusses his time in Rebbi’s court) he more often than other Amoraim argued with Tanaim since he understood them personally. So if an Amora could argue with a Tanna he could argue with an Amora especially if he lived at the same time.
The example given is where the Amorah argues with a Mishna in many places including Rav Nachman Ketubot 81b:
אמר להו הכי אמר רב יוסף בר מניומי אמר רב נחמן זו אינה משנה
which means that he can contest the opinion of the Mishna.
Examples of other Ammoraim who argue with Tanaim:
Rabbi Yochanan Kiddushin 9b who argues with Rebbi about wedlock through consumation:
ובביאה: מנא לן אמר ר' אבהו א"ר יוחנן דאמר קרא (דברים כב, כב) בעולת בעל מלמד שנעשה לה בעל על ידי בעילה א"ל ר' זירא לר' אבהו ואמרי לה ר"ל לרבי יוחנן כעורה זו ששנה רבי (דברים כד, א) ובעלה מלמד שנקנית בביאה
Shmuel in Megilla 7a who argues where we know the Megilat Ester was written with Ruach Hakodesh (Divine inspiration)
תניא ר' אליעזר אומר אסתר ברוח הקודש נאמרה שנאמר (אסתר ו, ו) ויאמר המן בלבו ר' עקיבא אומר אסתר ברוח הקודש נאמרה שנאמר (אסתר ב, טו) ותהי אסתר נשאת חן בעיני כל רואיה ר"מ אומר אסתר ברוח הקודש נאמרה שנאמר (אסתר ב, כב) ויודע הדבר למרדכי רבי יוסי בן דורמסקית אומר אסתר ברוח הקודש נאמרה שנאמר (אסתר ט, י) ובבזה לא שלחו את ידם אמר שמואל אי הואי התם הוה אמינא מלתא דעדיפא מכולהו שנאמר קימו וקבלו קימו למעלה מה שקיבלו למטה אמר רבא לכולהו אית להו פירכא לבר מדשמואל דלית ליה פירכא
Conclusion: Tyuvta on Rav meant Rav was subordinate to the Tannas opinion in that particular instance and chose not to defend his own opinion.
