1) Your question is asked by the Chavos Yair (Teshuvos, 192:17). He writes that it would appear from our Sugya that something was forgotten concerning the Halachah l'Moshe mi'Sinai, or that the Halachah l'Moshe mi'Sinai did not explain everything sufficiently. In his Teshuvah, the Chavos Yair cites many instances in the Gemara where there do seem to exist disputes concerning the above.

2) Before going further, we should mention a strong source for the axiom that you have cited. This is from the Rambam in Hilchos Mamrim (1:3) who writes, "Words of Kabalah never involve a dispute. It is known that if you will find a dispute in a certain matter, this has not been received from Moshe Rabeinu."

3) Towards the end of a very long Teshuvah, in which he asks many questions on the above rule, the Chavos Yair (page 559, DH v'Na) writes that one has to say that there is no dispute concerning the Din that one should add to the Shemitah year before it starts. However, the dispute concerns merely exactly how much time one has to add and other details that emerge from this.

4) See Sedeh Chemed (volume 2, page 287, DH Ulam), also in the name of the Chavos Yair and Shorshei ha'Yam, who says that the principle that there is no dispute concerning a Halachah l'Moshe mi'Sinai refers to a dispute concerning whether a certain matter is totally prohibited or permitted. However, it is possible that other less basic disputes exist.

According to this, it would appear that it is possible to have a dispute concerning what the source of a Halachah l'Moshe mi'Sinai is.

Kol Tuv,

Dovid Bloom

Here are additional sources which can help us understand how it is possible that there exists a disagreement concerning a Halachah l'Moshe mi'Sinai.

1) The first source is from the Talmud Yerushalmi at the beginning of the 4th chapter of Sukah. Rebbi Yochanan states there that the Din of "Eser Netiyos" (according to the text of the Korban ha'Edah) is a Halachah l'Moshe mi'Sinai. Later in the Sugya, the Yerushalmi cites Rebbi Aba bar Zavda in the name of Rebbi Chunya that this Halachah was from the "Yesod ha'Nevi'im" -- "a foundation of the prophets." (The Korban ha'Edah writes that this refers to Chagai, Zecharyah, and Mal'achi who lived at the beginning of the second Beis ha'Mmikdash period.) The Gemara wonders if it is possible that Rebbi Chunya disagrees with a Halachah l'Moshe mi'Sinai. The Yerushalmi answers that there was originally a Halachah in their hands but it was later forgotten, and then the second group of Nevi'im arose and agreed to what the original Chachamim had taught.

The Yerushalmi concludes that this teaches that whatever matter the Beis Din works hard on will eventually be established in their hands just as surely as it had been given over to Moshe Rabeinu at Har Sinai.

The Korban ha'Edah writes that the Halachah was forgotten by the masses during the 70-year exile in Bavel. Afterwards, the prophets at the beginning of the period of the second Beis ha'Mikdash reminded the people about these forgotten Halachos and therefore it was named after these prophets.

The Pnei Moshe appears to imply, slightly differently, that the Halachah was forgotten entirely, but then the later Nevi'im restored it by piecing it together again.

This explanation of the Talmud Yerushalmi appears consistent with what I cited in my first answer, that there cannot exist a dispute about whether the Din applies at all, but there can exist a dispute about the source of the Din. So, in our case, the Din was forgotten and afterwards was remembered. However, Rebbi Yishmael maintains that the Din was a Halachah l'Moshe mi'Sinai in the first place, while Rebbi Akiva maintains that it was originally derived from actual verses in the Torah. When the Din was later recovered, there still remained a dispute concerning its origin.

2) (a) I found an interesting interpretation of the dispute between Rebbi Akiva and Rebbi Yishmael in the Kapos Temarim to Sukah 34a (on Tosfos DH v'Echad). He questions Rebbi Akiva's opinion that Eser Netiyos is derived from verses: Do the verses in the Torah really make a distinction between old and young trees?

(b) The Kapos Temarim answers that since there is a hint in the Torah that one should add on to the Shemitah year in the period leading up to it, this means that the distinction between plowing the field for the needs of the young trees, or the needs of the adult trees, is included in the Oral Law, the Torah she'Ba'al Peh. Since it is hinted to in the written Torah, it is not considered to be a Halachah l'Moshe mi'Sinai. This is the opinion of Rebbi Akiva. However, Rebbi Yishmael maintains that there is no hint in the written Torah of adding to the Shemitah. Therefore, the Din of Eser Netiyos is considered to be Halachah l'Moshe mi'Sinai according to Rebbi Yishmael.

(c) It transpires that the dispute between Rebbi Akiva and Rebbi Yishmael is whether there is a hint to Tosefes Shevi'is in the Torah, but everyone agrees that it is not stated explicitly. If one says that it is not even hinted to, it follows that it is a Halachah l'Moshe mi'Sinai.

(d) Again, this seems to be consistent with the idea I cited in my first reply -- that a dispute may exist concerning the origin of a Halachah l'Moshe mi'Sinai, as long as the dispute does not concern the actual Din.

Kol Tuv,

Dovid Bloom