Volker Dusch has a new post reminding us about what the "unit" part of "unit testing" means - small chunks of testable parts in an application.
What does the word UNIT in unit testing stand for? Think of an answer and read on! So? Did you say "A method! Because we test methods!"? If so let me offer another perspective.
He suggests that, rather than about just the methods in the class, it's more about testing the "observable behaviors" of the class. That is, anything that you could publicly use the class for and have something happen. He gives examples of this shift in focus - calling setValue and evaluating the result versus just calling the class property itself (then calling the method). He also includes a bit about testing behaviors - what happens when my script does [this] and how does that effect the overall class.
When your tests fail but the class "still works" and you need to "fix the tests" the your tests are worth a lot less as they don't really give you that cozy safety net that they should provide you with.