This is true. There are lots of reasons not to use google's DNS servers. I will say though, assuming these things to be absolutely true, they really don't log anything that any DNS server would log, save random lifetime request record spot checks perhaps. According to their privacy policy:

"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 have to do this so that we can spot potentially bad things like DDoS attacks and so we can fix problems, such as particular domains not showing up for specific users.

We delete these temporary logs within 24 to 48 hours.

In the permanent logs, we don't keep personally identifiable information or IP information. We do keep some location information (at the city/metro level) so that we can conduct debugging, analyze abuse phenomena. After keeping this data for two weeks, we randomly sample a small subset for permanent storage.

We don't correlate or combine information"

They also state they gather this information as well:

"- Request domain name, e.g. www.google.com
- Request type, e.g. A (which stands for IPv4 record), AAAA (IPv6 record), NS, MX, TXT, etc.
- Transport protocol on which the request arrived, i.e. TCP, UDP, or HTTPS
- Client's AS (autonomous system or ISP), e.g. AS15169
- User's geolocation information: i.e. geocode, region ID, city ID, and metro code
- Response code sent, e.g. SUCCESS, SERVFAIL, NXDOMAIN, etc.
- Whether the request hit our frontend cache
- Whether the request hit a cache elsewhere in the system (but not in the frontend)
- Absolute arrival time in seconds
- Total time taken to process the request end-to-end, in seconds
- Name of the Google machine that processed this request, e.g. machine101
- Google target IP to which this request was addressed, e.g. one of our anycast IP addresses (no relation to the user's IP)"

[Google DNS Privacy Policy](https://developers.google.com/speed/public-dns/privacy?csw=1)

I think, if you care about having this independently verified (i couldn't find anything myself, yet) you shouldn't use them though. Its impossible to say if thats really all they are gathering. I've seen no evidence either way thats concrete. I will note though, that if they are, and of course right now its a big if just collecting the information above (which I imagine most DNS servers people use do anyway) as long as you are using their DNS API you could achieve higher level privacy with your DNS traffic.

From the Regional Internet Registry

"If applications made use of services that would push local DNS query traffic into encrypted TLS sessions, such as the service being offered by Google, the result would be that much of today’s visible DNS would disappear from view. Not only that, but it would make the existing practices of selective local inspection and intervention in the DNS resolution process far more challenging, if not infeasible. It may be even better if authoritative name servers were to also support queries over TLS and DTLS allowing a local host to take over the resolution function and still use encrypted query traffic services"

[Source](https://labs.ripe.net/Members/gih/dns-privacy)

They too note, however, privacy hasn't been independently validated on this front either. I would say if you care at all about privacy, not to use it, simply because its implications haven't been verified by a neutral 3rd party. At least, as far as I can tell.

Personally, I recommend using your own DNS server (I recommend the fantastic [Unbound](https://www.unbound.net/), and if you want to go 'full stack' you can pair it with [NSD](https://www.nlnetlabs.nl/projects/nsd/) ). and [DNS-crypt](https://dnscrypt.org/). That will give you more flexibility, potentially most consistent performance, and certainly better privacy, in my opinion.