I was having constant 403 hits in my logs, and from 127.0.0.1
It turns out that when I installed, I had copied the files from /usr/share/wordpress to my web directory /var/www/html/public/wp
In the configuration, I had set the main path to /var/www/html/public/wp as well.
Into the Apache config, the installation had added this alias:
Alias /wordpress "/usr/share/wordpress"
<Directory "/usr/share/wordpress">
Options FollowSymLinks
AllowOverride Options
</Directory>
Since my Apache root is /var/www/html, I changed the alias to:
Alias /public/wp "/usr/share/wordpress"
And the errors are gone. I hope this helps someone.