What's the document root setting in Apache config?
DocumentRoot "/var/www/html/moodle" ?
should be "/var/www/html"
If running Apache virtuals (more than one host from single instance of Apache), there are also documentroot's defined in virtualhost tags defining the virtual host.
Sounds like firewall is re-directing URL's which is messing with the config of Apache/Moodle. While using firewall to re-direct sounds good, it's not necessary as one can put a 0 second timelimit refresh auto forward default page (default.htm or index.html) located at the apache defined document root that auto forwards request to http://site/ to http://site/moodle.
< META HTTP-EQUIV="Refresh" CONTENT="0;URL=http://FQDN/moodle/" >
By doing so, Moodle is control of it's own and anyone accessing the Moodle from inside or outside the private network will be accessing the same (no apparent difference).
'spirit of sharing', Ken