To be fair, I did say this was in Chrome where you get find-as-you-type results.
And secondly, your ip address is not logged. The data sent to Amazon is via Canonical and it's anonymised. If you don't trust Canonical, why are you concerned about using a distribution from them?
Edit: I'm not saying there is no problem and I'm fine with all of this. Just that I wish better arguments were put forward (I'd personally like the functionality made explicit during install/upgrade)
If I enter analyze.com in the address bar and stop at anal, nothing happens. Nothing is sent.
If i enter analyse in the unity launcher and stop at anal, i get a nasty surprise and permanently get my ip address tagged with anal.