A misconfigured NAT rule in the Internet GW caused this error in my case, NOT a misconfiguration on the Linux host itself. Check for misconfigured or missing NAT rules in your Internet GW router!
I checked, double checked & triple checked all my local networking on the Linux host. I did comparative analysis with other Linux hosts in the same cohort; everything was the same. So why was this host's DNS now broken?
The answer was found in front of the host on my Internet gateway firewall. I had re-addressed several hosts (I know, never a good thingy ;->), but missed updating the NAT rule for this particular one in the Firewall. It was nothing at all to do with a misconfiguration on the Linux host itself.
But I got so blinkered about that DNS error message that I just assumed it was a misconfiguration of DNS on the host rather than on the firewall. Once I fixed the NAT rule, normal DNS resolution was restored. D'Oh!
So be aware that an incorrect or missing NAT rule for the affected host in your router can cause this error. HTH-