I've never used a proxy, so I don't know first hand how it's supposed to work, but if you log in with proxy settings, KoLmafia sets some System properties: http.proxyHost, http.proxyPort, http.proxyUser, and http.proxyPassword. Near as I can tell, ALL http connections that KoLmafia will make will be affected by those settings from then on. That would include fetching the faxbot config file. I don't think there's any way we can use a proxy for kingdomofloathing.com URLs and NOT use it for other URLs.
In other words, this smells like your system is blocking the Faxbot host, just as Winterbay suggests, making this a great big Not A Bug.