Watched a bit of this... It's typical test-driven zealotry; the main criticism of integration tests seems to be that they don't force your hand in system design in the way that unit tests do? Which seems very silly, but then, I'm not a person who goes to conferences about testing philosophy.
Did you miss his follow-up? "Integration tests are a scam is a scam". For real. I like J.B., but I think he muddies the water too much and overall understanding suffers.
https://www.youtube.com/watch?v=fhFa4tkFUFw