Yep this is exactly it I believe. I come from a very middle class background. My dad is  mechanic and my mom is a teacher. If I wanted to move up in the world this is the best route. I had neither the business connections nor the ability to afford an Ivy League school. That being said, I was lucky enough to go to a state school and for my parents to support me for about 6 months while I got my company making revenue. So your 2 conditions seem to hold true.