Unit tests don't guarantee that your code units are well designed. You can still write unit tests for spaghetti code. In fact, sometimes it encourages it because it encourages antipatterns like dependency injection; because developers get the urge to inject mock objects into the units from the unit tests.

Just think about it at a high level. If your module depends on another module, is it really always necessary that this module be substitutable for another module that has the same interface (e.g. another similar module or a mock)? 99% of the time, the answer is no! In fact it's often a problem because this wrongly assumes that if a class exposes the required interface, then it is compatible. There is more to compatibility than just interface; if the submodule maintains its own state (OOP), then its behaviour can change in a way which could break the dependent logic. You can't have Dependency Injection for everything because it's never so simple; these customizable parts of the code have to be designed very carefully.