I saw a lot of this as a student, and I'd like to add something to the mix, apart from the pure "Jimmy is John's boy, I like to play Polo with John, so ill sort Jimmy out" sort of connections.
Me and my siblings went to pretty much the whole specturm of schools as my parents moved around, from standard state schools, to some rather expensive schools. I feel this gave me a huge edge, not because my parents knew anyone, but because I had the confidence and knowledge to interact with anyone as an equal. Nothing makes you realise just how human a billionaire is, as yachting with them. Half the boats I crewed on I ended up being the guy telling the big shots what to do...
As I was finishing college, I went into interviews with relatively senior managers and could quickly figure out what sort of person they were and tailor my interviews to this. I left many, having spoken to them for the last hour about completely unrelated topics. I think my confidence sort of shone through, as I think I ended up with 3 firm offers and a 4th I turned down prior to it being an official offer. I had an OK degree (2:1) from quite a good UK college, so I probably would have been one of those kids you wondered about...
In my case it was definately not a case of knowing anybody, as I went to college and now work in a country my parents have never lived in.
I think one of the things most people forget about when it comes to finding jobs is that the itnerview is probably the single most important thing you do. Sure, grades matter, as does what college you went to, and extracurriculars, etc. But this only gets you an interview. After the interview you generally get solely picked on your performance in this. If you are a star on paper, but can't show it, forget about it. If you have an okay resume on paper, get an interview, and ace it, you are in.
In this regard, colleges do pretty much nothing to help students, which means that the more marginalised ones, regardless of skill or knowledge, will struggle if they cannot interview well. Often this is down to not being able to judge what sort of environment you are in/feeling intimidated/etc.