nobody does that

Used when someone claims that a set of people do something they generally don’t do or shouldn’t do

Person 1: Some people ride bikes on top of moutains
Person 2: Nobody does that.

nobody says that

Used when a person says something they claim a set of people say except they don't or nobody should say

Person 1: They say If you don't like the law, go somewhere else
Person 2: Nobody says that