I'm 99% sure the bag never went to baggage claim at LHR, because (a) otherwise the SAS staff would not have had any record of it and (b) more importantly, they likely wouldn't have been able to locate it so quickly.

I fail to understand why it's difficult to believe that both (a) SAS had the bag and (b) SAS neglected to put it onto the flight. Misdirected bags happen all the time.