The latter is possible, but cURL can't be the issue. The Steam Integration part uses a separate API and a separate method for obtaining the info. You don't even need a Steam Web API Key to use it. Anyone can access the data from that interface by just accessing the XML version of a user's Steam profile page. The interface in this plugin simply accesses that URL and pulls the Steam ID from the XML.
EDIT: We just did some more testing, and the issue almost certainly isn't related to this plugin, as he appears to be having issues accessing files on external websites altogether.
EDIT: We just did some more testing, and the issue almost certainly isn't related to this plugin, as he appears to be having issues accessing files on external websites altogether.