The file dialog enforces specific folders based on role permissions. The parameter passed in the dir param must be an allowed folder beneath his allowed starting folder according to the user roles otherwise it would be a big security problem if you could just pass in any folder as a query string param. The FileBrowserTextBoxExtender isn't really part of the security because it doesn't control uploading it just links to the dialog.
I don't really have a ready made solution for you to upload and browse to an arbitrary location. From your scenario it sounds like the person uploading doesn't need the dialog at all they just need to browse their local files and click upload and your code can put it in a specific place.
The existing file browser dialog allows admins to upload/browse beginging at the root /Data/Sites/[SiteID]
Users in General Browse and Upload Roles can upload/browse starting at the root /Data/Sites/[SiteID]/media
Users allowed to upload but only in a user specific location can upload/browse starting at /Data/Sites/[SiteID]/userfiles/[UserID]
So you could put your files in a folder under media and then the person who is making the links could browse to them using the link toolbar item in the wysiwyg editor (or using the FileBrowserTextBoxExtender) as long as he is in a general upload roles. The user who is uploading doesn't need to see where it goes and you can control where the file is stored upon upload from custom code, but putting it below media folder would make it eaiser to use built in features for the other person who is linking to the files, otherwise you would have to build your own dialog to browse and link to the file.
Hope that helps,