Your UI being off by a pixel won't break your application, so if a test hangs on that, then it is not a good test.
However, your business logic, or network protocol routine, those should not break even if you heavily refactor or add new features (especially business logic where a broken behaviour might seem correct), so those need to be heavily tested.
If it is hard to test the juicy parts like business logic without also dragging in the UI, different OS/platform/db parts, etc, then you should look at how your application is structured and if it is really optimized for writing good tests.