I agree with you, and for me the classification "integration" vs "unit" doesn't add anything. I'd rather distinguish between slow and fast tests.
In my opinion TDD is top-down (instead of bottom up) you must start with these things because you are not sure the abstractions you will have at the end. Your design and abstractions need to evolve from tests.
In my experience TDD is orthogonal to project design strategy. Whether your testable goals serve a bottom-up progression or a top-down progression, TDD is still a useful mechanism for advancing the feature set.
In my opinion TDD is top-down (instead of bottom up) you must start with these things because you are not sure the abstractions you will have at the end. Your design and abstractions need to evolve from tests.