Felix,
You should not assume that “invalid” and “failed” are the same. To me, “invalid” in this context is when a computer cannot determine with enough certainty whether a value is correct or not.
You get NAV AIR DATA SYS when both ADIRU and SAARU have no validated output. They are not failed however. The output is no longer the result of a blend of sensors. The ADIRU shows air data from the left pitot/static on the captain’s side and the SAARU shows air data from the right pitot/static on the FO’s side. The task of choosing which side, if any, is correct and taking appropriate corrective action is left to the crew.
The STBY instruments always receive data from the center pitot/static system via independent ADMs. The ADIRU and SAARU also use data from the center pitot/static sensors via their own ADMs so there is no complete independence here. The AIR DATA/ATT switch only serves to force the captain or FO PFD and ND to display SAARU or ADIRU single channel air data respectively and SAARU attitude instead of normal ADIRU data.
Hope this helps.
DJ.