I am assuming the prompt is for the username /
password for the domain. Internally you are likely getting through the
AD authentication check in your application as you will have permissions
to deliver the report (you can test that premise with Firefox or other
browser that doesnt handle AD authentication like IE does/
I think you may have setup for basic authorisation to view the report
RSReportServer.config rather than web.config is that what you have
done? (see this to see example http://msdn.microsoft.com/en-us/library/cc281309.aspx.)
If you are trying to get full anonymous access then you are in for
some fun; luckily one of the RS team blogged a way to achieve it; I
wouldn't advocate doing it straight onto a production box though.
http://blogs.msdn.com/b/jameswu/archive/2008/07/15/anonymous-access-in-sql-rs-2008.aspx