If anything, this transit/income data shows how little of a correlation there is between the two. This doesn't suprise me: most people in SF have cars, and muni/BART are embarrassingly awful compared to the big the cities in the US.
cities ==> city
The only big city in the USA with decent transit is NYC. San Francisco is comparable to Boston, DC, and Chicago and far ahead of LA, Dallas, and Miami.
By world standards, NYC is barely average and the rest of the country has no transit system at all to speak of.
I can count NYC as barely average only because the peer group includes not only London, Paris, Seoul, Tokyo, and Osaka but also Rio de Janeiro, Moscow, Istanbul, Mexico City, and Buenos Aires. If I'd just used your list, NYC would be dead last in almost every category.
The CTA is not. It's barely tolerable (and by tolerable, I mean that people are even capable of using it to get around and/or commute at all. So, the system might technically be a functioning transit apparatus, but barely.) I've used it daily for a sizable portion of my life, and it fails with remarkable consistency.