My thoughts are that it would depend on who was actually responsible for completing the review. Is the Safety department completing the review, in consultation with Ops, or is Ops completing the review, consulting Safety? In your case it sounds like the latter, in which case I would agree with your recommendation. If it was an initiative by the Safety department I would suggest they would be the owner.
I can completely relate to this type of situation by the way, in terms of the ongoing struggle of ownership in functional vs operations departments.
I hope that helps!