You applied this question:

When I modify this code, what tests will tell me that it still does what it's supposed to?

To this situation:

When I modify this code, will tests that enforce coupling between different components tell me that the code still does what it's supposed to?

You observed that no, such tests would need to be changed even though the overall logic was the same. I assume that next you would apply the same question to a test that is for the overall logic, and conclude that yes, it's a good test.