tests are supposed to improve maintainability. If you change a method and a test breaks that can be a good thing. On the other hand, if you look at your method as a black box then it shouldn't matter what is inside the method. The fact is you need to mock things for some tests, and in those cases you really can't treat the method as a black box. The only thing you can do is to write an integration test -- you load up a fully instantiated instance of the service under test and have it do its thing like it would running in your app. Then you can treat it as a black box.
When I'm writing tests for a method, I have the feeling of rewriting a second time what I
already wrote in the method itself.
My tests just seems so tightly bound to the method (testing all codepath, expecting some
inner methods to be called a number of times, with certain arguments), that it seems that
if I ever refactor the method, the tests will fail even if the final behavior of the
method did not change.
This is because you are writing your tests after you wrote your code. If you did it the other way around (wrote the tests first) it wouldnt feel this way.