First of all, the top 10% is nobody's definition of "the wealthy" -- that's what, ~100k? That's a single professional salary of someone who is doing well. That's a double-income family, where both parents have middle-lower class jobs depending on the area.
"The wealthy" that everyone refers to are the 1% -- hedge fund managers, CEOs, not doctors and engineers. Certainly not 100k/year households.
And the article and your argument both miss a fundamental point, which is not simply about income, but about wealth. The top 1% in the US owns 40% of the wealth. And for the ultra wealthy, much of their gains are not through income but rather through capital gains which are by comparison almost entirely untaxed.
The 'perception' comes from reality: you shouldn't frame it as if there is this false perception that exists and ask us to help you find out why, assuming your position is true and moving on without argument -- it is a true perception, it just isn't only based on income and on that arbitrary cutoff.
Also, "mid-2000s" (the graph that you linked) was a long, long time ago in terms of wealth inequality. It was before the great recession which devastatingly altered the inequality landscape.