I understand that you already received my reply in our Insights to the Daf, which included the same Derech as your Magid Shiur, besides much more. (My own suggestion was that a simpler mistake may have crept into Tosfos -- it said "Atzamos O Dam ," not Adam. (Blood can also be burned.)
Here's a copy of the full Insights in case you did not receive it, or lost it.
Be well, Mordecai
1) ASHES OF HUMAN BONE
QUESTION: The Mishnah (15a) says that as part of the Seder Ta'aniyos, they would place ashes upon the heads of the Nasi and Av Beis Din. TOSFOS (here and on 15b) writes that these ashes should come from a human bone that was burned.
How can Tosfos suggest using ashes of a human bone? It is prohibited to mutilate dead bodies. How can it be permitted to disgrace and defile human remains by burning it for this purpose? In addition, the remains must be buried, how can they be burned and placed on the heads of the congregants!
(a) RASHI (Berachos 5b) says that a bone less than the size of a barley seed does not need to be buried. If so, perhaps it may also be burned and it is not considered a disgrace to the dead.
(b) RAV S. Z. BRAUN in SHE'ARIM HA'METZUYANIM B'HALACHAH cites the MAGEN AVRAHAM (OC 311:3) who implies (perhaps based on this Tosfos) that the prohibition of disgracing a Mes does not apply if the body has been burned to ashes (see also TOSFOS in Chulin 125b, DH Yachol). Presumably, after being burned to ashes it also becomes a new entity and burial is no required.
Rav Braun, however, points out that many Acharonim do not accept this ruling of the Magen Avraham.
(c) The Acharonim ask another basic question. Tosfos says that we should use ashes of human bone to commemorate Akeidas Yitzchak. However, no human was actually burned at the Akeidah! It would be more appropriate to use ashes from wood or from a ram, since that is what was burned at the Akeidah. (KEREN ORAH, YA'AVETZ)
The SHE'ARIM HA'METZUYANIM B'HALACHAH suggests that there is a mistake in the Tosfos. Instead of saying "Etzem Adam," it should read "Etzem Ayil" -- "the bone of a ram ." (He proposes that in an earlier manuscript, the words in Tosfos read "Etzem A' " (Alef), and the printer erred and wrote "Adam" instead of "Ayil." Another alternative is that Tosfos originally read "me'Etzem O Dam " -- from bone or blood, since one may not waste food by burning meat for this purpose) Since a ram was burned in Akeidas Yitzchak, a bone from a ram should be burned to arouse Hash-m's mercy by alluding to the Akeidah. (See Rosh Hashanah 16a "Blow before me the Shofar of a ram, that I may remember Akeidas Yitzchak.")
QUESTION: However, according to all of these answers, Tosfos is saying that a specific type of ash should be used. How did Tosfos know that a specific type should be used? If anything, it can be inferred from the Sugya on this Daf that any ashes may be used: The Gemara records an argument between Rebbi Levi bar Chama and Rebbi Chanina whether the reason for putting ashes is to remind us of our worthlessness -- we are like ashes -- or to remind us of Akeidas Yitzchak. The difference between these two opinions, says the Gemara, is "Afar Stam" -- dirt. According to the opinion that says the point is to remind us of our worthlessness, we may also use dirt, while according to the opinion that says that the point is to remind us of Akeidas Yitzchak, dirt does not suffice.
If, as Tosfos says, the opinion that connects the ashes to Akeidas Yitzchak holds that ashes of bone are required, the Gemara should have offered that as the difference between the two opinions as to the reason for placing ashes. According to the one who says it is reminiscent of the Akeidah, it must be ashes from bone , while according to the other opinion any ashes may be used. Since the Gemara did not offer this as a difference between the two opinions (but mentioned dirt instead), it seems clear that ashes of bone are not required! (BIRKEI YOSEF OC 579 and Acharonim)
ANSWER: Tosfos said that the ashes are from bones to answer another question. How can one opinion insist that ashes are put on the people's heads to show that "we are worthless as ash," and therefore dirt may be used as well as ash, when the Mishnah clearly seems to contradict this assertion. The Mishnah mentions specifically that "Efer Makleh" (ashes) was used, adding the word Makleh to exclude dirt, as Rashi explained in the Mishnah? (KEREN ORAH, RASHASH)
In addition, the Amora'im that discuss the source for placing ashes seem to be arguing over a subject that is already debated by the Tana'im. On Daf 15b the Gemara brought a Beraisa in which the Tana Kama writes that plain "ashes" were used, leaving out the word "Makleh" (and thereby including dirt). Rebbi Nasan argues and says "they would bring Efer Makleh ," meaning specifically ashes. Why didn't the Gemara just say that the debate of the Amora'im over why ashes are used was already debated by these Tana'im?
Because of these questions, Tosfos understood that when the Gemara says that the difference between the two opinions is "Afar Stam," it is not referring to dirt. The word "Afar" here means ashes (as in "Afar Serefas ha'Parah," see Rashi in the Mishnah). Both opinions among the Amora'im permit only ashes to be used. The argument between them is whether a specific type of ash must be used, or any type of ash may be used. The opinion that says that the point is to remind us of Akeidas Yitzchak holds that only the ashes of bones may be used, while the other opinion allows any ashes. If so, both opinions concur with the ruling of the Mishnah, and with Rebbi Nasan of the Beraisa.
In fact, this is clearly implied in the wording of the Gemara, as we have it in our texts. The Gemara says that they argue whether "Afar Setam' may be used (plain ashes). Rashi (DH Afar) says that the word "Setam" is extra and should be erased, since it makes no sense for the Gemara to refer to "plain dirt" as opposed to some other type of dirt -- what other dirt is there? Tosfos, on the other hand, makes a point of saying that the Girsa Afar Setam is correct. He explains that the word Afar means ashes, and not dirt. When the Gemara says that the Amora'im argue whether " plain ashes" may be used, it means as opposed to a specific type of ashes; ashes from bones. (M. Kornfeld)
(According to the other Rishonim, who learn that dirt may be used according to the Amora who says ashes are placed on the head to make a person feel worthless, how can this opinion be reconciled with the Mishnah, which says specifically "Efer Makleh" is used?
1. They might explain that the reason it says "Makleh" (ashes that come from a furnace or from a normal fire) is to exclude the ashes of a Parah Adumah, as one opinion in the ME'IRI learns. (This is apparently the opinion of RASHBAM in Bava Basra 60b, DH Efer Makleh.) . One might have thought that ashes of a Parah Adumah must be applied to be Metaher everyone, so the Mishnah emphasizes that any Efer can be used. The Mishnah does not write Makleh to exclude dirt, and dirt may also be used. The Tana Kama of the Beraisa, though, insists that ashes of a Parah Adumah are applied, for the above reason.
2. Rashi, who does not explain like the Rashbam, offers a different solution (15a DH Efer), as the LECHEM MISHNAH (Ta'aniyos 3:1) KEREN ORAH and RASHASH explain. Rashi implies that even if dirt may be used, since it also denotes worthlessness, nevertheless it is better to use ashes, which display even more worthlessness (since they are not fertile).)