Do you mean that the case described in the original post was a "secret girlfriend" situation? If you do,I guess that in the very strictest sense of that term,his wife *was* his secret girlfriend because her existence hadn't been revealed to the new "fiance".
But were he and his wife living together at the time? Were they sleeping together? Divorce proceedings *had* been initiated..and were almost complete.
Unless there's something that I'm missing here..or that hasn't been disclosed in the article...I'm not sure that she has the *moral* right to keep the ring.