"Most single mothers start from behind; they're less likely to have a college education or a high income. Single motherhood is a lot less prevalent in higher-educated women. This college gap exists for white, Black and Latino families."

These seem to be things to control for before making a causal claim. I haven't read the original study, but wouldn't be surprised if they didn't control for these (and other) important factor because then they'd likely not reach their desired result.