Except there isn't a double negative in this translation due to the comma. If it was "No one does not do that" then yes, it would be a double negative and incorrect. With the comma, it is equivalent to "no, no one does that" or "no, nodody does that". In this example it's like "no, [some]one does not do that". "one" refers to a single person of unknown or unspecified gender. If that makes any sense.
Do refers to the action involved, and make refers to the results.
You do the cooking, but you make the meal.
You do your homework, but you make the grade (pass the course).
You do the planning (for an investment), but you make the profit.
You do exercise and you make yourself feel great.
"Ingen gjør det" means "Nobody does that." For example, watering a sidewalk to try to fix it. There's no point. It doesn't work, so nobody does it.
When you say, "One does not do that," it means people in general shouldn't do "that." It's a sentence that a parent or teacher might say to a child who has done something inappropriate or wrong.
Here are some examples:
One does not spit on the sidewalk. (It's inappropriate and dirty.)
One does not throw garbage out the window of a car. (It's littering and illegal.)
One does not hit classmates. (It's hurtful and doesn't solve problems.)