Testers find bugs that users don't find

It is hard to admit it, but many times we testers find bugs that a user most probably won't find.

For instance, I am testing piece A that is designed to work with piece B.
They seem completely independant, but in real life they are used always toghether.
However I, as a tester, set up piece A and test it immediatelly (unit testing, remember?).

It fails. I find later it only works when opiece B is correctly set up and working.

A system administrator would not go across this, because he would set up piece A and pice B then would try the system...