The participants were not asked how happy they were, they were asked where they stood on a 'satisfaction ladder' with the best life they could imagine at the top. Many people may be perfectly happy, but they know their position on the wealth scale and imagine that they would feel more satisfied at the top of that scale.
people are actually pretty bad at defining where they are on the wealth scale. For example, loads of very rich Americans seem to think they're middle class (the WSJ once portrayed a middle-class family as earning $100000 a year, which actually places them in the top quintile).
What you call a misapprehension I would instead call "identifying a delusion." The faux-classlessness of American society is one of the weirder and to my mind deleterious aspects of the American character, in part because I think it feeds into Steinbeck's temporarily-embarrassed-millionaires phenomenon (the rush of actual middle-class people to defend the people who will profit from their defense).
And I don't think it holds true, anyway. I don't have the same problems as someone making $25,000 a year (approximately the 48th percentile as per Wikipedia), though they are recognizable to me in the abstract. I also don't have the same problems as someone making $200K a year and they are utterly foreign.
$100k/year is very much in line with what an actual sociologist would describe as middle class. Most of the upper quintile is part of the middle class. Most sociologists describe the top 1-5% as upper class. The next ~45% is middle class, then the next 30-40% is working class, then the remaining 10% or so is poor/lower class[1].
The upper class is made up of capitalists, high-level executives and people with inherited wealth. People who work in professional occupations such as doctors or engineers are not part of the upper class.
Another way to interpret it is the higher your income, the less you expect to be able to advance in the future on sort-linear-log scale. Or the poorer you are, you tend to feel poorer (than you actually are) on a sorta log scale.
There are no poor people in America, only temporarily inconvenienced millionaires.