Any experience with lunch breaks and time sheets?

A friend of mine is having some issues at their job. They're really happy with it, but they've been required to do two things. By law, they have to have a 20 minute lunch break, but the amount of work they get requires them to work through lunch or have a short lunch or go home late.

They don't mind this, but because of a legal requirement for a 20 minute lunch break they have to put on their time sheet that they took a lunch break while not actually taking a break.

So they work through lunch but don't get paid for it because the law is trying to help them.

Any experience here in dealing with things like that?