I think it's not false. I think trust is a pretty generous word, too generous, to describe how most people feel about using Facebook, even if they enjoy using it.
Further, I believe most people who are even the least bit savvy about data mining on the internet use Facebook with a certain air of resignation: their kids use it, their parents use it, their real friends and relatives use it, etc., and they all chide you if you don't sign up to use it too... your refusal to sign up means they end up having to email you, or they have to set up dropbox links for party photos.
Many don't think about it at all, so at best it's "trust by default" -- because they're young and may think it doesn't matter to have it "all out there".
And some have even bought into Zuc's wayback statements about the concept of privacy itself being "so over"... when he was first rolling Facebook out to the public. If you bought that idea, then in my book you weren't a trusting sort of person, just gullible in allowing someone else to redefine a perfectly good word.

by the way i think it's hilarious how Wikipedia starts out its entry on Privacy. I am not sure that Mark Zuckerberg would be as amused.