You are correct on score. I see what you did there on saying some credit card companies ask for docs and others don't. Correct BUT they do ask. Whether you tell them the truth is up to you. I have a buddy who has never had a job and always tells them he makes over $200,000 a year as an author and he now has like $80,000 in available credit.
I know I am correct about the scoring model and again, income documentation and debt ratio has nothing to do with it so not sure why you mentioned it in the first place in the context of credit score
regarding income "docs" you can't really lie when providing docs (i.e. not tell the "truth") unless you're fabricating pay stubs, W-2's, etc..
stating a false income on an application is another thing altogether (what you said your buddy did) does not count as providing docs. Docs = verification of income
not only have I have never been asked to provide a shred of income documentation for any credit card, I'm pretty sure I wasn't asked for anything when I got my last car loan (99% sure since it's been years since I got an auto loan).