This is a completely idiotic statement that demonstrates an utter lack of understanding of how the internet works in 2012.
Whenever you search for anything, Google knows that YOU have searched for it. If you search for a suicide hotline or online forum that helps suicidal teenagers, Google will know that you, specifically, have searched for it. If you go onto a website that displays Google's adverts or uses Google's analytics and software (which is pretty much every website - bbc news and wikipedia are the only ones in my favourites that don't track you), Google will know that YOU have been on that website. If Google ever decided to, it could let the whole world know that you are a suicidal teenager. Or what kind of pornography you enjoy. Or that you have erectile dysfunction. Or that you have a mental illness. These are the kinds of things that can destroy marriages. These are the kinds of things that you can lose your job over. These are the kinds of private information that should never be held without your consent. Did you consent to Google knowing your entire browsing history?
You don't need to "put" anything on the internet for it to be recorded for all time. Nearly everything you have done on the internet for the past 5 years or so is recorded somewhere, and it's all traceable back to you.
On a side note, if you have a browser with a decent script blocker, like Firefox with NoScript, you can block Google Analytics to lessen the effect. You can also turn off Google History, though I have no idea if that actually helps in any way.