I think it's generally understood that signed documents describing the terms in detail is what matters. In my mind, integrity is a) not lying about what's in the docs b) sticking to the letter and spirit of signed docs. Until docs are signed, there is no deal
Integrity: "I like your offer a lot" (but then something actually changed, and I don't sign).
Lack of Integrity: "I'm in." (but then I don't sign.)