How is household income always the same number as personal tax liable income, especially when it comes to a dependent?
You are misunderstanding this.
We are discussing what Amex considers to be reasonable access, and that is what is filed on a tax return, regardless of status such as joint. I know people that have included a relative's income because they live in the same home, and Amex does not include this income in a FR.
Definitions vary by issuer.
You can search for BobWang's thread on this subject on CB.