Fortunately, they do preserve the original file as /etc/named.conf.applesaved. I merged the two files together (which resulted in my original file with two new lines.) These two new lines refer to a file /etc/rndc.key, which doesn't exist. Furthermore, without /etc/rndc.key, BIND won't even start up! So I commented off those lines.
As the article (see link, above) says, you should do this even for a clean installation. I assume this rndc.key file exists on Mac OS X server. Either way, if it doesn't exist, the named.conf file must not refer to it.
The Tiger installer also trashed my startup script (/System/Library/StartupItems/BIND), but as it turns out, this doesn't matter, since Tiger doesn't use it anymore. Instead, it uses plist files in /System/Library/LaunchDaemons. A plist for bind (org.isc.named.plist) is created by default. A default installation has this disabled (at least according to the above article), but in my case, it was enabled. I assume the installer saw that I had it enabled in my 10.3 installation and therefore enabled it for 10.4 as well.
Anyway, it was a relatively minor problem to deal with, once I realized what happened, and it was easy to fix. Hopefully, this message will help out anyone else that finds himself in this situation.