Yes, I trust that Google has not shipped a binary modification to their open source software to track search terms, which would be (a) illegal, (b) easily detectable enough that someone would notice it eventually, and (c) pointless, since they're already getting the vast majority of users' search terms legitimately. Then again, I work for them, but I would have said the same thing a month ago...
Agreed. I just searched "PRISM" on DDG, and 8 out of top 10 results had some element loaded from a Google server (GA, fonts, jquery, search box, embedded youtube, etc.) Are you using Google's DNS server? Google owns the web. Face it.
You don't have to trust it. You can sniff 100% of the traffic coming out of your own computer. You can even configure a firewall to block all traffic to Google's netblocks.
edit: Missed the suggestion to block traffic entirely with a firewall - thought the discussion was only on sniffing traffic. Less ridiculous then :)
You're suggesting people that already stated a distrust in Google do a thorough network traffic analysis after every update, so that they know their privacy is violated after the fact? That's a bit ridiculous, really.