I think you've badly misunderstood the paper and its results and are taking some sort of Occupy Wall Street mindset... The 'gradients' the paper is talking about are not exotic gradients which apply only to the general population vs the 1% of the 1% who get into an accident in their Lamborghini and call their dad in the Bahamas who deploys a crack team of white-shoe lawyers to ensure he never appears in court; it's talking about the health gradients you see when you compare the first decile of income nationally to the second decile, the second decile to the third, the fourth decile to the fifth, and so on. (AFAIK, the Swedish administrative data doesn't even give access to the 1% as they topcode or withhold access to their data.)

You see health differences no matter who you define as 'richer' or 'poorer', throughout the general population, in ordinary people. Yes, in the normal people you pass on the street, who have no 'financial advisors' other than their uncle who has some hot stock tips (although I suppose he would count as 'inherited'), who have no 'people investing their money' unless they are unusually prudent and have some Vanguard savings, who are not 'able to afford universities and good health', and so on. The person making $5k a year is less healthy than the person making $20k a year is less healthy than the person making $50k a year, and so on. Where are the monocles and secret cultural rituals there? None of these people 'grew up rich', so you should still see benefits when the $20k person wins a few thousand bucks in the lottery, if the causal effect here is through the money. But you don't.