So the pyramid argues that you should do much more automated testing through unit tests than you should through traditional GUI based testing. ref
I always argue that high-level tests are there as a second line of test defense. If you get a failure in a high level test, not just do you have a bug in your functional code, you also have a missing or incorrect unit test. Thus I advise that before fixing a bug exposed by a high level test, you should replicate the bug with a unit test. Then the unit test ensures the bug stays dead.