I'm actually already using a server-side proxy. As the article you linked suggests, Silverlight won't make cross-domain calls. In other words, your client app won't call into
www.wowarmory.com directly. Instead, it makes a request to the WowProphet host which makes the Armory call on its behalf.
As for why you're having issues behind a proxy, I haven't been able to find any resources about issues with Silverlight and proxies. I'm unable to reproduce the problem, but I'll add it to the list and see if anyone else has similar issues.