Seat assignments
 

I have a AY6 JFK-HEL flight coming up in April - with Mrs CKBA.

I'm BAEC Gold, with the ticket booked through AA and was automatically assigned a seat in Y+. Mrs CKBA, BAEC silver, was booked through BA, but couldn't get a Y+ seat (without payment). I changed my seat to sit next to Mrs CKBA, but it seems that she should have been able to get a Y+ seat for free. Correct?

Correct.
http://www.finnair.com/fi/gb/flights...lect-your-seat
You can select a seat free of charge in the following cases:
- You are a oneworld Emerald or Sapphire member (reservations through Finnair Customer service).

Certainly works with my silver card, I flew HEL-JFK this week in economy comfort. Visit manage my booking on AY website and choose the seat. Economy comfort seats are free.

The same for HEL-LHR a few weeks ago (they use an A330 on sunday mornings). Economy comfort was free for me on that flight also (although their seat selection page promises long haul benefits like amenity kit, which are not given out on economy comfort HEL-LHR).

And last year LHR-HEL on the A330 in the second business cabin since they were selling it as economy. Again free of charge with the BAEC silver (Sapphire) card.

In AY terms Sapphire is (was) quite a high level. Even AY ruby level included lounge access in HEL and Sapphire includes premium lounge access. This changes soon though (lounge access lost for AY ruby level). I was wondering why I was shown the way to the premium lounge even with BAEC silver!

Premium lounge is for all OWS and OWE, not only AY's own.