I ended up cutting through the nipple to get it replaced:
http://s23.postimg.org/fuo8c0qqf/IMG...917_135256.jpg
You are right, the threaded ring is brass and the pipe segment is copper and connected to the inside of the ring by sweating.
The first couple of turns of the female thread on the waste stack outlet, where that brass threaded ring was, are relatively clean and can be used. The rest are covered by the buildup of either rust, or hardened sewage deposits.
Can the rest of the female thread underneath that buildup be cleaned to be used or it's pretty much gone?