Hullin 131: Are the Levites Part of the Jewish People?

A particular levi would grab the gifts going to the kohanim, before they reached the kohanim. The people complained to Rav... which raises the question of the gifts that are not required of the levites for the kohanim. But why aren't they required of the levites? Where does Rav find this approach? The difference seems to hinge on whether the levites are part of the people. Also, any foods that are considered sacred are taken from the levites, but not the things that are not sacred. But at the end of the long discussion, it seems that Rav's view is refuted, and the levites really did have to give these gifts.