There must be a procedure. EU Laws also require the operating airline to provide refunds. If a passenger ticketed by AA is downgraded by BA, then BA will work with the ticketing airline.

SG could provide a refund under their calculations. If not, AC is ultimately on the hook for the refund. If both refuse then it's up to the purchaser to take action and start a legal claim possibly based on how much SQ or AC sell miles. Things usually get settled at that point.