Eugene, There was absolutely no US immigration paperwork at my starting point. Besides, since I don't need any visas or entry permits to enter the US then how can there be any possible paperwork?
JonNYC, It is my opinion that upon seeing my AA award ticket the AY check-in agent changed his opinion on the check-in time. He didn't seem to have any problems with starting the check-in. The problems started only when I presented my AA tickets.
Furthermore, I must say that the whole Finnair approach to AA ticketed flights is somewhat hostile. On a number of occasions I have tried to get some help out of AY agents from their main city offices in the Northern and Eastern Europe but as soon as they see American issued tickets then they try to explain to me that only AA can help me with anything at all. They have even gone to the extent of telling me that there are AA offices at Helsinki airport and Arlanda airport!!