The article repeatedly uses what it calls a "true tax rate", which is calculated from wealth. It does this knowing that people reason about tax rates as percentages of income.
With this in mind, I think it's fair to say that the article puts a fair amount of work into talking about wealth and income as different, but also willingly conflates the two in order to produce shocking numbers when it's convenient.
If you look at Scrooge McDuck's giant pit full of gold coins, and even though the pipe flowing into the room marked 'income' doesn't have any coins rolling down it into the pile, but the pipe heading out marked 'expenses' seems to be steadily draining coins... and yet the pile of coins is somehow still getting bigger...
.... maybe you have to accept that just looking at what's going on in that income pipe isn't giving you the whole picture.
I don't disagree with anything you've written here. I just think that conflating growth in value of assets and liquid cash is misleading, and using a snappy sloganeered idiom to do so compounds the error. That this is done in pursuit of illustrating an absolutely critical and nuanced political point about finances makes it, in my opinion, all the more important to be clear.
I recognize that this is a position with which reasonable people might differ.
Use more graphs?
Call out incomes (wages, dividends, rent, etc) and assets (property, investment) differently?
So you end up with these wealthy people spending a ton and increasing their net worth by huge amounts, and paying small (or zero!) taxes.
I agree with you that a different tax law that calculated owed tax like this would not be completely reasonable, but it certainly shows the inequality and I believe it's a reasonable alternative. How would you measure the tax impact on the mega-rich otherwise?