It's always interesting (in a sad way) when a programmer or DBA comes to me with a basic networking or Unix question that any CCNA or RedHat candidate could answer. Then I get a very safe feeling about my job security when they start asking me if I could look at their code. This has happened too many times in my career.
People seem to equate broad knowledge to mean you're a jack-of-all-trades-and-master-of-none. These are usually the same Comp Sci PhDs that have no clue why they just got fired for saying something totally inappropriate in front of HR.
The more knowledge you have about anything and everything that your systems interact with then the better you will be at your specialty.