Brain,
  Here is a my steps for setting up the Proxy to bypass the login (they are a little different from that post).
1. Here is my proxy.config. Notice I am using username and password and not clientId and clientSecret:
EDIT: but I just tested with clientId and clientSecret and it works fine that way too.
<?xml version="1.0" encoding="utf-8" ?>
<ProxyConfig allowedReferers="*"
             mustMatch="true">
    <serverUrls>
        <serverUrl url="http://calhoun.maps.arcgis.com"
                   username="username"
                   password="password"
                   matchAll="true"/>
        <serverUrl url="http://services.arcgisonline.com"
                   matchAll="true"/>
        <serverUrl url="http://gis.calhouncounty.org"
                   matchAll="true"/>
        <serverUrl url="http://gislap183"
                   matchAll="true"/>
    </serverUrls>
</ProxyConfig>
2. My config.json is basically the same:
"httpProxy": {
    "useProxy": true,
    "alwaysUseProxy": false,
    "url": "/WAB/Proxy/proxy.ashx",
    "rules": [{
        "urlPrefix": "http://calhoun.maps.arcgis.com/",
        "proxyUrl": "/WAB/Proxy/proxy.ashx"
    }]
  }3. My app registration is basically the same:
URL: http://gis.calhouncounty.org/ MY apps url (removed for obvious reasons)
API: JavaScript
App Type: browser
Purpose: Configurable
Redirect URI's: http://gis.calhouncounty.org
The big thing about step 3 is that the item is PUBLIC (the app item that you are registering). The webmap is still private and secured though.