Following https://groups.google.com/d/topic/bigbluebutton-users/cHu6b2KJl3Q/discussion and https://code.google.com/p/bigbluebutton/issues/detail?id=1419
it turns out that BBB Recordings plugin sends an extra long URLs to BBB server when retrieving the list of records for a particular course.

The reason it is doing that appears to be due to having groups in a moodle course that uses BBB recordings. With groups, each recording lookup is multiplied by the amount of groups. In our case the course had 10 groups, so 10 extra requests for each recording was added to BBB recording lookup and as a result - 14 recordings was enough to go over standard 8K size for GET requests both in nginx and tomcat.

The place where groups are handled appears to be at mod/recordingsbn/view.php, lines 114-118. Eliminating them reduces the request size significantly...