you have enough assets to generate income that allows you to live an upper middle class lifestyle without having to work for the rest of your life. "Independently wealthy" I guess.
Well, I would call that "independently upper middle class". To be distinguished from rich.
But the topic here has nothing to do with taxes or past data.
With respect, we have been discussing both topics. I reported IRS data on the distribution of AGI. But this does not let one conclude who is "rich." You can define the top x% as rich, but what is the basis for that? If one were to ask "is everyone in the top 0.1% of income or networth rich?" I gather your answer would be "yes." my answer would be "I don't know, how much money is that?" I don't have the data, but I am pretty sure I would be in the top 0.1% in Somalia or Haiti. But that does not make me rich, here or there.
when people think of their income, they do not typically think of AGI
I do. In part because I can compare this over the years to IRS data. But my wife constantly tells me I do not think like other people.
AGI is a good, standard, and quite reliable measure of income. You can calculate precisely. People have to report it and the IRS audits it. One may debate whether it is comprehensive enough, but everyone can agree what it is. Any income measure that includes imputed income is immediately suspect because you have to decide how much income to impute. To pretend that this is actual income received by any individual is fanciful. No one knows the real value. This means you have to be very careful in claiming to know where someone sits on such a measure. The broader "economic income" used by the TPC includes "returns to capital", which they simply declare to be 6% of networth.
One could use the broader measures of income if you could find one that was as reliable as AGI. AGI also has the advantage that each individual calculates his/her number every year. I can look up my history of AGI, and I can compare my AGI trajectory to that of the nation as a whole. I cannot do that for "cash income". Not only do I not trust their imputed figures, but I have no way to reproduce them. So I cannot know what my cash income might be.