I'm a little surprised that SSH authentication methods can't be easily disabled using the sshd_config file. Almost all the other security algorithms can be easily tweaked. I thought this article had just made a mistake, but I read over the man page and it appears there is indeed no way to modify this using the config file.

This isn't a protocol weakness. Reading over the SSH RFCs, the server is allowed to specify which algorithms it supports, so this could easily be a OpenSSH configuration option.