Their DNS privacy policy seems acceptable to me, as they’re not using it for ad data: https://developers.google.com/speed/public-dns/privacy
Google obviously has many concerns, but they’re trustworthy enough to follow their own privacy policy lest they get smited by governments.
Example: They can see that I have visited Wikipedia, but not what articles I’ve read. (Other sites will leak more info due to the nature of their subdomains, but it doesn’t bother me personally.)
lots of hits on hackernews and jsoneditoronline.org and I can say with a reasonable degree of certainty that you're in IT or Dev. gonna start sending you ads that reflect that.
likewise, hits to missile-gayboy.jp -- a site that used to be hosted by my old employers -- also sends some pretty clear messages. I don't need to know what you're looking at specifically there but it's a japanese site that caters to a specific niche; I can sure make some assumptions.
hell, at work we don't even collect a lot of specifics on our endpoints -- domain queries are often enough to catch bad behavior