The description about Mr. Cleany-Clean is wrong because:
1: None of the school staff can tell the difference between garbage and usable items. It doesn't matter what you litter in the corridor, you will be punished.
2: He says "trash is true evil." Seriously, if he had greed, he would care about the things you drop and maybe even take items from your hand.
EDIT — Oh yeah, and the school staff have no way of knowing who dropped anything despite you being the only one doing that. I've never tested this, but I'm pretty sure that if you just stand there with the knife and parts in front of you on the floor, none of the teachers would care less.
Also, Mr. Mix wants to actually cook the food ("Oh! What time it is! It's time to cook some food.") and judges you as a chef, so something's probably going on while the spelling is happening. Also you're not allowed in his kitchens, and the rest of the cafeteria is empty.