One thing to keep in mind here is that many web sites, even internal site, load content from other servers. If they are trying to load ANYTHING from another location, you will get the log in prompt.
For instance, we have www.hp.com in our whitelist. That mean you do not have to be authenticated to get there, but when you go there it loads different content on other servers than just www.hp.com. Hitting cancel many times lets the page load, but it will be missing some stuff.
Try using Fiddler and watch what else is loading when you hit the web site. http://www.fiddler2.com/fiddler2/
This is the type of application what I exactly need!
Aside from bypassing the external websites I also reconfigured the webwasher since there are redundant authentication settings were present.