I think you're missing an important piece in your summary. The original page-rank algorithm was based around the idea of authority. A site might contain content entirely relevant to your query for cancer, but if it has no authority then its probably not what you're looking for.

But this no longer works because the original indicators of authority have died out as the web has become less of a network, since search enables everything to exist in isolation (at one of my work sites we just trimmed the majority of the links from our site).

But if you can determine which people have authority, then you can use their browsing habits in order to allocate authority to websites again. Instead of website having and giving authority, you start giving an authority (per topic) score to users, and then use their behaviour to determine authority in pages.

This last aspect is, I think, what jacques is pointing out, and its not that the social graph gives relevant results (which as you say, everyone knows about), but that it gives a different mechanism for authority (which yields better relevance).