"We use our in-house analytics system, by the way, because we don’t wantto give the engines our data. For many of our clients, however, we just install Google Analytics, since it’s easy, cheap (free), and has a beautiful UI."
With Google's Adwords revenues soaring (pretty much every 4th online ad dollar ends up in Google's pocket) and
since Adsspy.com is able to figure out related sites based on your Google Analytics code (which is an open door for any competitor), I tend to say that I would stay away Analytics software, that is provided by a search engine.
I certainly cannot proof Harrison's concerns, but it is just at a point where you are probably better off running Sitemeter, Getclicky, Omniture or some other system, which is not affiliated with your ad spent.