I do not know if AY pays a fee for passengers using the priority lane? Most likely not, since the BPs are not scanned. Scanning of them takes place at many other airports, which could result in separate fees for the airlines. There is a similar situation for *A passengers at ARN, CPH, and OSL, which has aggravated many travelers.
Luckily, at HEL the normal security lines are quick to pass and sometimes using the priority lane actually takes more time. There are many sunday-flyers, indeed, among the users of fast-track security almost everywhere, wondering what it is all about, and finally realising that they should have checked in the kitchen sink...