Today I forgot that Postfix runs in a chroot by default on Debian. If you change files like /etc/resolv.conf or /etc/hosts, it has no effect on Postfix, unless you refresh the corresponding files in the chroot. Wasted quite a few minutes before the clue bat descended and gave me bruised ego. Stopping and starting Postfix (with postfix stop and postfix start respectively) provided the clue as the start command helpfully reminds you that the chroot is out of date.
It's good thing that this was on my own server so there was no customer watching me chase a problem caused by forgetfulness. Must be getting old. ^_^