I was not aiming to define what a unit test is, more like when it stops being a unit test (which I thought it would be an easier agreement to reach than a definition of what is, but I guess I underestimated the task).
My point was that if you have to mock, for example, a DB call inside your business logic, well you are writing an integration test at that point, whether or not you mock the DB out. If you design your code so that you only have those dependencies at the edge of the system then you get, in my opinion, a much cleaner design and much more testable code.
Too much mocking (and/or more like mocking in the wrong places) is a code smell in my opinion.