Linux is the operating system of your server, you should know how to use it. Apache is your web server, you should know how to set it up and configure it. The same for your database MySQL. Obviously you had better know PHP(Python if that's what your P stands for) to develop any software.
I think you're mixing up Full Stack developer with Application developer. The application developer would take PHP and connect to a database to make the application and that's normally that. The full stack developer would set up the servers, configure them, create the application, deploy it, and all that jazz.
I'm not saying one is better than the other. You get more flexibility with a full stack developer but you can get more expertise with an application developer. It all boils down to the opportunity cost of having someone who can do everything well or 2-3 people should all be experts at their part of the puzzle.