Still seems like a problem to me. It breaks encapsulation.
The mutex is only used inside of SetAlive() and isAlive(), they're the only things this need to handle locking and unlocking. You don't want anything external to that calling the methods on RWMutex.
Oh of course, if you're not using it then don't expose it.
I haven't read the code so I can't verify if that's the case here, but I read OPs post as being worried about method clobbering (which is really a non-issue, if the popularity of embedding mutexes shows us anything).