It's open source. Since it sounds like you won't trust Canonical's claim on this anyway, why don't you take a look, or ask somebody who can, instead of creating fear about it?

If it turns out that searches leak out despite the setting, I'm sure you'll hit the front page of HN. Since this hasn't happened, and Canonical have been under considerable scrutiny about it, I think it's safe to say that your conspiracy theory doesn't hold up.