I have no idea what goes on in google. That said, even if they don't correlate with "personal information that you have provided," you as an IP address are stil

I have no idea what goes on in google. That said, even if they don't correlate with "personal information that you have provided," you as an IP address are still identifiable as that IP address, and correlatable with yourself, for as long as that IP lasts for you. Which means Google could cause ads to follow you around, for example. Again, I don't know what all they actually do or don't do with their DNS logs, but the quoted "promise" doesn't promise anonymity, just separation of you as a known Google user from you as a semi-anonymous but specific DNS user. I'm reminded of the early days of the Snowden revelations, when the NSA was saying "it's just metadata."