If you can provide a link to the sources you have seen it might help. I won't be surprised to find that a reasonable understanding of that caption turns out to be true, but I will still criticize it for being sloppy. I mean to say: is income disparity inherently bad?Your question to disprove their statement also doesn't take into account inflation.
About the caption beginning "almost all of the income ..." I only said it is not clear. I can't say if it is true or false, because I don't know what the author means by "almost all" or how "the richest Americans" are defined. It looked to me like the numbers behind the chart were adjusted for inflation, but I am not sure which graph you mean.Income disparity is the biggest (?) problem in the economy today because it tends to render moot any and all fixes to the economy that the Fed/whoever can come up with.
You are saying that income disparity is serious because it stops us from fixing other problems. What are the problems you would like to see fixed? If we could fix those problems and income disparity continued to exist, would it still be a problem?