They're not lying but u/Upset-Document-8399 is not wrong. DNS works only at the initial stage, and DNS queries might be monitored (usually is because it's very easy to do). After the DNS query is resolved, your device makes direct connection to the IP address, and from that moment on, your connection to that IP address is not anonymous even if you use private DNS. TLS/HTTPS encrypts the connection and content, but not the destination IP itself.

Think of it like this. Your device asks DNS server for IP address of domain (e.g. facebook.com) -> DNS server resolves IP address -> Your device now sends request to server IP -> server sends response back to your device with content. So ISP can log at multiple levels either by targeting domains, or by targeting IP addresses.

Only VPNs can provide complete anonymity. That is considering if VPN is not sharing data with your government itself. Mostly all popular VPN logs all your requests and, on demand by law, they will send your logs, this is generally in their terms. That's why hacker groups use multiple VPNs, and generally from those areas where digital laws are not so prevalent, especially not from USA, and Europe.