I have a MOSS 07 site that is configured for anonymous access. There is a document library within this site that also has anonymous access enabled. When an anonymous user clicks
Using a tool like Fiddler (as referenced/suggested in your first link reference, see http://www.fiddlertool.com/fiddler/ for more info) is the only efficient way of determining the root cause of this type of issue I'm aware of. Whatever is causing this will be happening over HTTP. A debugging proxy like Fiddler will show you exactly which URL/resource is causing the request for authentication.
On a related note, are you running a recent build of the platform? It might be wise to check to make sure this issue hasn't already been addressed by MS e.g. in a hotfix. The best list of updates I'm aware of is here: http://www.harbar.net/articles/postsp1.aspx