Albert Barnes Commentary Leviticus 16:26-28

"And he that letteth go the goat for Azazel shall wash his clothes, and bathe his flesh in water, and afterward he shall come into the camp. And the bullock of the sin-offering, and the goat of the sin-offering, whose blood was brought in to make atonement in the holy place, shall be carried forth without the camp; and they shall burn in the fire their skins, and their flesh, and their dung. And he that burneth them shall wash his clothes, and bathe his flesh in water, and afterward he shall come into the camp." — Leviticus 16:26-28 (ASV)

Both the one who led away the goat and the one who burned the parts of the sin offerings had to purify themselves. Those who went out of the camp during a religious solemnity incurred uncleanness; therefore, there was a need for purification.

(Leviticus 16:27) Shall burn in the fire—that is, consume in the fire, not burn sacrificially. See Leviticus 1:9.