I understand your logic.
However, where is that logic stated on the Star Alliance website?
I am reading that statement on
http://www.staralliance.com/en/benef...silver-status/
3. This benefit may only be available if travelling on two or more Star Alliance member airlines on a single ticket. Please contact the Star Alliance member airline with whom you will check-in with for further details.
As I read it, there is no legal right for the status passenger to receive one free bag.
I mean I am venting about the LH group policy, as well. LH still offers very expensive one-way fares (e.g. LHR-FRA-VIE), where the LIGHT fare ticket costs almost EUR 500.