I have to agree that the bread and butter lies with where the front sight is when the hammer falls. If you put a weapon on a vice, the only thing that matters is that the sight picture is correct when the firing pin strikes, not how the vice is holding the weapon or how the vice is breathing when the trigger is pulled.
The same is true when a person is holding the weapon. However, we are not rigid vices. Grip, breathing, stance all MAY or MAY NOT aid a person in holding the proper sight picture throughout the duration of the shot. The sight picture is what matters most, but the ability to maintain it depends on all the little things the shooter has to do to impose that disclipline upon him/her self.
For me, personally, grip and stance matter the most in keeping my sight picture aligned. I barely qualified on the 9mm Beretta in the Navy. I started in a Modified Weaver with a really crappy grip. My buddy the Gunner's Mate showed me how I was wrenching the weapon and how applying the preassure to the front and rear of the weapon and sliding my finger out of the trigger guard and applying "straight back" preassure to the trigger would help me greatly. It certainly did and it wasn't long before I qualified Expert and maintained it throughout my Naval career. I soon became Duty Gunner's Mate and Range Master qualified and was responsible for small arms training the entire 4 years that I was embarked aboard the ship.
Fast forward 11 years and I'm qualifying on the same weapon with the Coast Guard instead. They tell me that I have to stand an Isosceles position because studies show that it's the best position for new shooters. I play ball, but I find myself in an extremely uncomfortable (for me) shooting position. I barely qualified! I didn't realize it then, but what Ranger SXT said about back spasms happened to me. I thought I was just nervous because I was in boot camp and didn't want to get yelled at for not holding the proper position.
In closing, the sights are what really matter, but being a mere human, it is difficult to maintain that picture without the aid of a proper grip or stance or controlled breath or whatever else you need to do to deliver little hunk of metal to the little black dot.