Sorry but that`s just not the case. It`s a myth propagated some time ago that has developed into popular belief. The vast majority of single barrel flintlock sporting guns had straight grips - likewise single trigger double-barrel guns.
The straight grip became universal amongst English sporting guns because of the type of shooting it was most used for. When you have little idea of when and where a bird is coming from the straight grip allows for faster mounting and handling. When you do know pretty well when a bird - or clay - is coming ( and where from ) the gun can be pre-mounted and a pistol grip makes sense.
Anyone that allows the grip to move through their hand on recoil is asking for a smack in the face from the stock - the trigger finger moves, NOT the hand.