How is it "not extremely strong"? If there were no correlation, you would expect the top 1% of income earners to hold 1% of net worth, because there's no expected relationship between being high in income and high in net worth. If there were a correlation but a weak one, you might expect them to own a few times the uncorrelated amount. Maybe they'd own 2% of U.S. assets (twice the otherwise expected amount), maybe even 5% (five times the expected amount). Either of those would be enough to establish a clear relationship, but a weak one.
But they actually own 26% of American assets, twenty-six times the amount you'd expect in the uncorrelated case! The top 1% of Americans by income own a full quarter of all the country's assets— stocks, bonds, real-estate, etc. That seems like a pretty strong relationship.
This just isn't good statistics. The fact that the vast majority of hysterectomies are performed on women doesn't tell us anything about the probability that a randomly selected woman has had a hysterectomy; the fact that the vast majority of wealth is held by the rich doesn't tell us anything about the probability that a randomly selected rich person has a lot of wealth.
Err, the fact that the vast majority of hysterectomies are performed on women does tell us that hysterectomies are strongly correlated with sex. That was the initial dispute: whether wealth and income are strongly correlated or not. The distribution is a separate argument, although I'll note that the PDF I linked has some data on the distributions as well, and it does not support the "weak link between them" argument. The proportion of very-wealthy people with low incomes, and very-high-income people with low wealth, is actually quite small.
I took a quick crack at the correlation implied by table 5 in that paper you linked. Assuming wealth was constant across the ranges specified, I came up with a correlation of 0.45. So meaningful but not high. I personally suspect that it's actually much more highly correlated and that fact would come out if I didn't have to assume wealth was constant for 0-50 and 50-90, but it would be conclusory for me to incorporate that into my numbers.
