Your business logic tests will already, by osmosis, exercise the backing data store in every conceivable way to the fundamental extent that is possible with testing given finite time. If that's not the case, your business logic tests have cases that have been overlooked. Choosing SQLite does mean that it will also be tested for code paths that your application will never touch, but who cares about that? It makes no difference if code that is never executed is theoretically buggy.

Business logic tests will rarely test what happens to your data if a machine loses power.