>but I figure the majority of content on YouTube is genuinely owned by the people who post it, while I very much doubt this is the case on Pinterest.
That assumption seems fairly inaccurate, see this quote:
"Remarkably, more than one-third of the two billion views of YouTube videos with ads each week are ... uploaded without the copyright owner’s permission but left up by the owner’s choice." [1]
Didn't read the article, but as far as I can see that doesn't disprove his assumption.
The NYT quote is talking just about the videos with ads, and then only discussing them in terms of views (not in terms of percentages of actual content uploaded, which is something like 24+ hours of content every minute).
That assumption seems fairly inaccurate, see this quote: "Remarkably, more than one-third of the two billion views of YouTube videos with ads each week are ... uploaded without the copyright owner’s permission but left up by the owner’s choice." [1]
[1] http://www.nytimes.com/2010/09/03/technology/03youtube.html