mmm well here's the thing and the difference. It depends on what you want to test. You want to test the AP/function of a single table? that's a single component.. which might still be composed by different pieces, but that's still a component.
So that's a unit test... an integration test instead would be exactly what we are doing right now with SQL. An integration tests gets nearer to what a user sees.. also, if you wanted to test the gen* function of a table, you could call the function directly (with a unit test), vs passing through different systems (sqlite sql planner for instance) to get your answer.