The conclusion I have reached is that the AY e-ticket system is incompatible with the e-ticket system of other OneWorld airlines. And since AY do the ground handling for BA in HEL, the AY system cannone "see" the e-ticket issued by BA/QF etc. Possibly the same problem for LHR checkin on an AY e-ticket, in that the BA agents cannot see the AY system e-ticket.
But don't AA claim to be able to e-ticket AY flights (in fact all OneWorld flights)? So perhaps there is a link between AA's Sabre and whatever AY use, but BA and QF do not yet have that link established?