Cunliffe,
It wasn't insurance the answer is on this page, the A to A scenic flight requires an AOC, therefore the pleaure / scenic flight needs to cover the AOC cost hence the increased price.
I use to work for flying school with an A to A scenic flight operation. Before I could fly on the scenic flight I had to do an OPC (in a 172FR) with an examiner, all the ground stuff (ditching, first aid, dangerous goods, security etc), but as an instructor I could still fly the same plane in the same airspace from the right side with as you say a complete stranger and novice at the controls as a trial lesson.
So it is not just the cost of the AOC registration itself, but also the additional pilot ground training and opc costs that also adds to the cost of running an A to A AOC.