Also, ideally your code and test are somewhat independently written, whether it is whitebox or blackbox. If that is the case,you greatly reduce the chance that both the code and the test are wrong in such a way that the test still passes.

This is why writing unit tests for stuff like getters and setters is really dumb. It doesn't really simplify checking whether the code is correct unless you use something like meanbean and thus provides some degree of separation between the test and the implementation.