It does.
For some reason "code testability" is almost exclusively used to refer to the overuse of dependency inversion to make it easier (although not necessarily more useful) to write unit tests, though.
I find that code falls into three camps - integration/logical/mixed.
If it's integration code only an integration test is really useful and a unit test is a pointless waste of time that will do little more than mirror the code you wrote and fail when it is changed for any reason at all.
If it's logical code a unit test is most useful and integration tests are likely going to be too slow.
If it's mixed, integration tests are most useful although drawing out and decoupling the logical from the integration code and testing them separately is better in the long run.
