It's not a 100% overlap, nor is it the only contributing factor, but it is a factor none the less...
People tend to excel when given the opportunity to pursue the field(s) that interest them...when you drastically limit the fields available to them, the chances of them pursuing a worthwhile career path are going to, in turn, be limited as well.
For example, I hate doing physical labor, hate getting my hands dirty, etc... I don't mind physical activity, I love weightlifting, running, etc... However, if you ask me to paint, do yard work, manual labor, work on cars, etc... that stuff is absolute torture for me. I was fortunate enough to go to college, so I'm able to do what I actually enjoy for a living, which is working with software and computers.
Had college not been an option for me, I'd have been screwed because I would've been lousy at any job involving manual labor (likely been fired for not giving it my all, or not inspired to even apply for those jobs at all) and as a result, would probably be working retail or some mundane job making 1/5 of what I'm making now.
That same narrative certainly applies to a large percentage of the population. Everyone wants to find a job their well-suited for and enjoy doing to at least some degree...every job is work, but different people find different forms of work enjoyable or at the very least, tolerable.
When you take a group of people (referring to people from low income households) and say "everyone else is getting to choose between those 100 career paths...but for you, you have to pick from these 12", it's no wonder that the group has more people in poverty situations because you likely have more people who are facing the choice of "pick something you absolutely hate, or be poor"