Indispensable & work of excellence?

I had a very interesting discussion with a friend today, let's called her A.  Some background of the story.  A is your typical employee that most boss will like.  She will not draw boundary, as long as she can do and the boss asked her to do, she will do.  For eg.  If A is a retail assistant, she can be helping at the loading bay, or clearing rubbish, or helping out at the display, or checking stock, anything, as long as she can do it!  So typically A works late night, because she will be doing everybody's job.

And the discussion came about because A was sick, quite seriously sick, running a high fever too.  But she still insisted to go to work, because she thought that the office will fail to function if she is absent. 

Part of the conversation goes like this
Me:  "You are sick.  Why are you still at work?"
A:  "Because the programmers are doing a system upgrade"
Me:  "Oh, i didn't know that you are a programmer!"
A:  "No, i am not"
Me:  "Err..then what are you doing in office"
A:  "To make sure that the programmers do their job, so that the system will work on Sunday"
Me:  "Do you know IT?  Have IT background?"
A:  "No"
Me:  "Then you should wait til the UAT"
A:  "Yes, i will do the UAT, but now i need to be here to make sure there will be UAT"
Me:  "So you think you are indispensable"
A:  "I need to ensure work of excellence"
Me:  "Why don't you just ensure your area?"
A:  "Then how to have work of excellence?"


???!?!?!
I was totally bewildered.  Never know that someone can have so wap idea of indispensable & work of excellence.  So if the CEO need to ensure work of excellence, he will be monitoring all issues, from minor to major ones.  How to cope as a CEO??
Anyway our "debate" goes on, but i will not go into details.  Just thought that it is a very strange thought to think that one is so important and indispensable...The earth will not stop turning because of one person, isn't it?  A person will be missed, but definitely not indispensable...