The study defined middle-class households as those making between two-thirds and twice the national median income. That was roughly $42,000 to $125,000 a year for a family of three in 2014, though adjustments were also made for the cost of living in different areas.
I can't imagine a more biased definition of "middle class" than that. Fact is, $125,000 puts a household firmly in the top 20%. That's hardly middle class. Using the Wiki/Census, I'd say median income ±half median income. Median is $57,000, so the range for middle class is $28,500 to $85,500, which puts the top of the middle class in the 69th percentile or upper 30%. That makes a good deal more sense.
In any case, the notion of middle class was originally based on population distribution of income, not income percentiles alone. The phat middle was the point, and was what drove growth. As income/wealth has increased its skew, growth has waned. It's not a coincidence, but even Bernie (that I've read, anyway) ignores the historical record.
Here's a particularly helpful post. Note the median and average incomes shown in the bottom right of the graph, as it changes. This is the cumulative income distribution, so you don't see the skew of the frequency distribution graph, but when the average/mean is above the median, that's the definition of right skew (aka, income inequality).
And, it turns out, The Donald has changed his tune (now that he's got the nomination sewn up) on taxes: bunches for his 1% class, of course.