The issue was in the /etc/default/bind9 file indeed. The culprit: OPTIONS="-f -u bind"
I honestly can't remember why the -f option was there. It must have been needed for a (perhaps much) earlier version of bind9. Up until now, it worked without problems, but I guess that the new method for signaling init changed that? I suppose running in the "foreground" is a strange option to use for a daemon.
In any case, reverting to the defaults solves the problem.
