Yes, they do not PERMANENTLY store PII, because they are crystal clear about the fact that they store it temporarily, and that by that they explicitly say they mean 24-48 hours:

> Google Public DNS stores two sets of logs: temporary and permanent.

> The temporary logs store the full IP address of the machine you're using.

> We delete these temporary logs within 24 to 48 hours.

> In the permanent logs, we don't keep personally identifiable information or IP information.

"Permanently" is not weasel-worded here.

So they do permanently store some information, perhaps tied to everything that isn't PII: my location, connection speed, time of day, access frequency. That can certainly be used to target adverts.

When an easy alternative is a company that doesn't have a reason to store this data, why not choose them?

By all means, choose whomever you trust the most. All I was saying in my response above was that, in making that decision, it would probably make sense to make sure you're reading their privacy policies accurately first. In this case the idea that "permanently" was weasel-worded seemed incorrect and misleading to me.