The posted link covers ntfs security qtrees/volumes and does not apply to you.
The parent directory (where A_dir is) is writable by user B. When you were trying to do stuff in A_dir, you couldn't because A_dir's permissions were too restrictive. Removing the directory is an operation in the parent directory, not the directory you're trying to remove, so the parent directories permissions govern. A bit goofy, yes....
Deletion without permission only happens when you perform above step on a directory on filer (mount). If you perform above steps for a directoy on Linux server, permissions works fine (i.e. you are not able to delete dir for which you don't have permissions) even though parent directory has permissions for all users.
That is interesting. On my Redhat 5.5 boxes I can remove dirs without permissions, as long as I have permissions to the parent dir. What OS are you running? I'm assuming no sticky bits, no extended file attributes, and so selinux? Also assuming none of your test users are root?