You're probably also more able to work if your folks make enough money to have a stay-at-home parent (so you don't have to watch your younger siblings), buy you a car to get back and forth from your job, etc. Without seeing how they actually did this study, I'll go ahead and chalk most of this up to generational privilege.
Hmmm I'd want to see some data on this before drawing any conclusions, because my anecdotal experience is the opposite. The poor teenagers I knew pretty much all had jobs, in large part because they needed the money. Their only option to be able to buy new clothes or a used car was to earn the money themselves. Well off kids didn't have that same sort of pressure.
My first job as a teen was delivering newspapers (not sure that's really an option anymore, though). I also cut lawns in the summer. All of that was on foot or bicycle. Didn't have a car until I was 18.