- The Meiri writes in his introduction to Avot that this is an example of the Ammoraim disagreeing with the Tannaim which they would occasionally do if the Sages of the generation agreed. So that would be option (c):
ועם כל זה נתמעטו הלבבות מרוב הצרות והוצרכו האחרונים לחבר אחריו דרך ביאור והרחבה ולפעמים דרך סתירה ותיקון כשהיו חכמי הדור מסכימים לכך ממה שרואים בו קושיא חזקה...וכן אמרו פרת חטאת אינה משנה...וכן תמיד איתמר חסורי מחסרא ...וכן הרבה כיוצא באלו כמו שנעשה היום אף אנחנו מראשינו וזקנינו הקודמים ועוברים לפנינו ועל ראשינו וכמ"ש דרך כלל מקום הניחו לנו כו' כלומר שאין השלימות נמצא בנבראים ואפי' במובחרים שבהם עד שלא יהיו אחרונים רשאין לחלוק עמהם בקצת דברים
Similarly, the P'at HaShulhan of R. Yisrael Shklover cites the Vilna Gaon as opining that it is a way of disagreeing with the Mishna. However, unlike Meiri he adds that this was in following a variant Tannaic view. However, he does not say that that view had to be expressed in a Mishna, nor does he say how they knew it was a Tannaic view. The book Kol Eliyahu, however, claims he did not say this, but rather that they explained the true intent of the Mishna (a variation of (a), see below for many who espouse this position).
- The opposite sentiment is expressed by Rabbenu Bahya (Exodus 34:27) who emphasises that the expression does not connote any shortcoming whatsoever with the Mishna. Rather, it indicates the Ammoraim's shortcoming in that they failed to properly understand the Mishna:
ומזה אמרו בתלמוד על המשנה: (ברכות יג ב) חסורי מחסרא והכי קתני, שאין הכוונה להיות המשנה חסרה כלל חלילה, אבל הכוונה שהיא חסרה אצלנו מפני חסרון שכלנו מפני שאין אנו מגיעים לעומק חכמת דור של חכמי המשנה, ולפיכך עשו רבינא ורב אשי פירוש על המשנה והוא התלמוד ובארו ספקות המשנה והאריכו לשונם על לשון המשנה העמוק והסתום
He makes no mention of (a), clearly eschews (b), and the Meiri's (c). Rather, he seems to be explaining a variation of (a); that people were lacking in their ability to understand the Mishna, until they finally understood it. (Not that the Mishna necessarily intended to be brief, to facilitate memorization, or for some other reason).
R. Yeshaya Horowitz writes very similarly in Klalei HaTalmud (10: Klal lamed: 205) in the name of the Sh'erit Yosef (Netiv HaMishna Klal 5) in the name of R. Mattityahu Hatsorfati.
- Similarly, Hida writes in Shut Tov Ayin (3: Note 10) that it is clear from the Zohar (Raaya Mehemna Parashat Tsav 207b) that the expression means that the author intended to be brief and included the full idea in less words, not that something was actually left out. This is basically (a). (Except that he makes no mention of memorization. This differs from R. Bahya, R. Horowitz, et al. in that he specifies that the Mishna itself intended this brevity).
Prof. David Weiss HaLivni writes similarly in Midrash, Mishnah, and Gemara: The Jewish Predilection for Justified Law, page 92.
- Rabbenu Yeshua Halevi writes in Halikhot Olam (2:2:14) that one can only apply this to a small change not a big change, since a person would misremember a minor point, but not a major point:
חסורי מחסרא והכי קתני, ודוקא להוסיף אבל להחליף הדבר בהפכו לא...משום דאדם טועה בגירסא לחסר דבר על ידי שכחה אבל להחליף דבר בהפכו לא
This indicates (b). Specifically, the reference to טועה בגירסא indicates a transcription error, rather than an originally mistaken ruling.
Significantly, elsewhere (3:2:14) he contrasts חסורי מחסרא; which involves emending the text of the Mishna with other methods which merely explain the intent.
This is also clearly the view of the Hikrei Lev (Vol. I OH 12) who writes that this idea clearly indicates the the Mishna was not written down, since otherwise one could merely compare printed versions of the Mishna to resolve the textual issue.
The Tifferet Yisrael to Arakhin (Boaz 4:1) writes that the Mishnayot were associated with tunes to facilitate their memorization. For this reason the Mishna would sometimes leave something out, or phrase something in a particular way, to match the tune. This is a variation of (a). (In that it is to facilitate memorization, but he says nothing about it being internally obvious that something is left out.)
Another variation of (a) is that of R. Yosef Karo (Klalei Hag'mara to Halikhot Olam 2:2): that there was memorized Mishnaic literature that preceded the compilation of the Mishna. Some mistakes crept into the memorized texts. When R. Yehuda HaNassi compiled the Mishna, he left these corruptions, and relied on the readers to correct the mistakes. (This is basically (a) with the twist that originally it was a mistake (as in (b)), but by the time the Mishna was compiled, it was deliberate).
See Mevo L'nussah HaMishna (here) by Prof. Yaakov Nahum Epstein for a lengthy discussion and a survey of the classical views on the topic.