It's actually really hard to create well-performing AI in a first person shooter, unless you give it explicit access to the internal state of the game. See: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=612949...
I mean do we want all AI endeavors to be towards believe-ability or being best at the job they're designed for?
They might not even be mutually exclusive. If you give an AI the same handicaps as a human, it would likely behave in a very similar way.
That is handicaps like delayed inputs for reaction time. Fuzzed outputs so it can't time movements absolutely perfectly. Giving it limited amounts of training on the game so it can't get extremely good. And requiring it to play the game through the same user interface. So that it can't see things humans can't or micromanage 50 different things at once.