You'd be surprised. Consider the effort many game studios go through to get the testing done on a game before release. It is a pipe dream to think that everything can have a full automated test suite written for it. I suspect that the only things this is true for, are things which have been written so many times as to be almost trivial. (Not that we don't make enough mistakes on those systems...)

Though, maybe you were just questioning the "perfectly" portion. I mean "perfectly" in the sense of "validates all of the user's requirements." Not in the "covers all paths" or "anticipates all possible scenarios."

Consider, crash test dummies. This is a form of testing that is far far far more expensive than having a complete model of the system. Yet, we still do them. We do not rely solely on them, you say? Of course not. Apologies if it sounded like that was my point.

Edit: Also, it is also possible to use traditional QA tools without having a fully dedicated team. That is to say, unit tests are not a QA tool. Yet, we constantly try to replace the QA team with them.