The corner and edge pieces are guaranteed to have the right orientation, but the center pieces can be in any 90° orientation. Imagine an arrow printed on a center piece; a cube can be solved and still have that arrow pointing to any of the 4 neighboring sides.
Here's a video explaining special algorithms to rotate only the center piece: https://www.youtube.com/watch?v=fk1eCZNCTB4
Ah, interesting, thanks! So it's possible to reach a configuration where every side has the centre rotated but all the colours match up. I would not have believed that without seeing it.
I don't understand this. If you have a corner piece in the wrong corner then won't the colours on the adjacent faces be wrong?