When I try to align the gun right down my right arm, I suppose my arm does better at fighting/absorbing the recoil, but my head is cocked so far to the right to look down my arm, it feels very un-natural.
It is un-natural. He's not the first expert to say this is important, but to not actually do it . Yes, at 2:00, you can see him demonstrate an in-line barrel when he's not actually in a shooting position. Go to 5:30, though, and you will see that barrel is certainly not in-line. Looks like a standard isosceles stance to me.
I was only referring to target shooting, and the question was only about precision.
You can mess with other grips and stances, but for 2-handed accuracy, a neutral grip/stance is best, IMO. A neutral stance is where your grip and stance isn't itself influencing the gun. Imagine getting in your shooting grip/stance using a piece of tissue paper instead of your gun. Imagine a grip/stance where the tissue between your fists isn't put under tension, and certainly not ripped. Your fists can be quite tight and controlled without tension on the tissue paper. There may be some variations on it, but IMO, for accurate and/or fast 2-handed shooting, the isosceles stance is the way to go. And I don't know if he mentioned it or not, but thumbs can influence the gun as well, so I keep them forward and off the gun entirely.
gun should be in line with my right arm, so the recoil goes right down my arm
You can't really "control" recoil, so a stance and grip which sends the recoil "straight back into your arm", is not only not neutral (i.e. not the best for accuracy and/or speed), but doesn't address the real issue, which is whether the front sight returns to it's starting position at the end of the recoil cycle. Since a neutral grip isn't influencing the gun, the front sight should return properly. This is a big reason why those uber-fast runNgun guys use this stance & grip - they don't have to consciously re-align the sights after a shot - instead, their sub-conscious just confirms the sight picture and bang.