I still feel the overall point attacking the statistics of income inequality is much more likely to be used as a gavel to silence those working to improve the status quo. Articles like this are often cited when people try to take action to correct income inequality, regardless of what the article ultimately advocates.
That said, I do think its important to get the statistics correct. I don't think you said anything wrong (except maybe with your definition of gini, as others have noted). Your headline is a bit salacious, but ultimately my concern is how this article might be used by others.