What version of ArcGIS Server are you running? While I can access the link you provide, none of the links from that page work, which means to me that you've only exposed the one page publicly. If you are running an older version of ArcGIS Server, having the server behind a firewall can be problematic. For example, I can't access the ExportMap link on the page. Since you have a tiled map service with a coordinate system that doesn't match, arcgis.com will make an ExportMap call, instead of accessing the tiles.
Mike