I think the point is that if you have to change a test to make it pass or run after refactoring, it is not useful as a regression test. By changing it you might have broken the test itself so you have less confidence.

There is also the question of what a unit is. If you test (for example) the public interface of a class as a black box unit, you can refactor your class internals as much as you want and your tests don't need to change. You have high confidence you've done it correctly. At this point adding more fine-grained tests inside the class seems like more of a compliance activity than one that actually increases confidence, since you probably would've had to change a bunch of them to make them work again anyway.