I changed the title in 2010, because the phrase "integration tests" was not accurate. I changed it to "integrated tests" to clarify my position as I have explained it to you.
As you say, it is challenging to achieve 100% integrated testing. (I assume that you mean this.) I agree, so I don't try to achieve it. Instead, I verify that each layer can talk to the next layer correctly using special kinds of unit tests. I can do this at every layer from the beginning of the system to the end. I have been writing about these techniques and teaching them for 15 years. It is difficult to explain in only one paragraph. :)