The right mental model for using mutexes: The mutex protects an invariant.
Why are you sure that this is really right mental model for using mutexes? I think right model is protecting data but not invariants.
The problem of protecting invariants presents even in single-threaded applications and has nothing common with multi-threading and mutexes.
Furthermore, if you need to protect invariants, you still may use binary semaphore wich is never recursive.