Here's a better analogy: Imagine your employer requires you to work some night shifts, just to have someone on premises in case "something" happens. You and your employer both agree that often nothing happens, so you can in fact sleep during those night shifts. But your employer says that sleeping on the job is not work and therefore should not be paid.

The European Court of Justice held that the employer is wrong, and if they require you to be on premises, even if sleeping, that's work: https://en.wikipedia.org/wiki/Landeshauptstadt_Kiel_v_Jaeger (this was related to European laws, of course, not American ones)