What is "Or ha'Olah ... Lo Yih'yeh" coming to preclude?
Rashi: It precludes a T'vul-Yom, a Mechusar Kipurim and an Onan (who are not eligible to offer on the Mizbe'ah) from receiving a portion in the skins of Kodshei Kodashim. 1
See Sifsei Chachamim.
On what merit do the Kohanim receive the skins of the Kodshei Kodshim?
Oznayim la'Torah: They receive it as a gift from the Table of Hakadosh-Baruch-Hu, not as remuneration for their services 1 ? which they provide 'free of charge'.
Oznayim la'Torah: Because if it was in the form of remuneration, why would a Kohen who sacrifices an Olah receive only the skin, whereas a Kohen who sacrificces a Chatas ? which requires less Avodah (See Oznayim la'Torah), receives in addition, the Basar of a cheap Kisbah (if that is what the owner brings), and one who sacrifices an Asham, which requires less Avodah still (see Oznayim la'Torah), receive, on addition, the Basar of an Ayil? On the other hand, the Oznayim la'Torah adds the Ma'aser which the Levi'im receive, is remuneration for the Avodah that they perform in the Ohel Mo'ed, as the Torah specifically writes in Korach, Bamidbar, 18:21, which explains why they may do with it whatever they please.
What about the skin of a Chatas and an Asham?
Ramban #1 and Moshav Zekenim #1 (citing Zevachim, 103a): They too are given to the Kohen, 1 since, like the Olah, they are Kodshei Kodashim.
Ramban #2 and Moshav Zekenim #2: Since the Kohen receives the Basar of the Chatas and of the Asham it stands to reason that he also takes the skin , and the Torah only needs to teach us the Din by an Olah, whose Basar he does not receive.
Zevachim (ibid.): As opposed to the skin of Kodshim Kalim, which the owner retains. See Torah Temimah, note 9.
