Opportunities like OP described are not as rare as all that. I grew up in an agrarian town but was able to access a lot of the resources of the nearby university through programs like the Cooperative Extension Service. They are not things that fall in your lap, you need to find them and take part; but you don't need well connected or educated parents to get them.

No. I grew up in inner city, poverty, single parent. Believe it or not most scientists are extremely generous with their time and these programs do exist for students who seek them out.