Seems spurious. Could be talented people move to cities with high earning potential—which happen to be walkable. Do the authors control for that?
It's as if a study came out that showed that, according to their exhaustive statistical analysis, people that drove Mercedes tended to be wealthier than people who drove Chevys. Then they concluded that the key to upward mobility must be to get a Mercedes.
But I agree that it's very unlikely to be that being able to walk places makes you succeed. Could even be something as simple as enough people owning a few flats in their neighbourhood, which suddenly became super-valuable when lots of google employees showed up. That would look a lot like income mobility.
>We 1st identified the relationship between walkability and upward mobility using tax data from approximately 10 million Americans born between 1980 and 1982.
Reading the abstract, it looks like the authors are trying to make a causal argument: people are more likely to improve their economic standing because they moved to a walkable city.
OP pointed out that this could be due to self-selection of people with the potential of upward mobility to walkable cities. This would lead to spurious correlation between economic mobility and walkability. That is, a third variable (a potential candidate, awareness of climate change) could explain both upward mobility (usually, climate change awareness correlates with education level) and economic mobility (education correlates with higher wages).