To me, the y axis in the controller is forward, not up. So push head forward to look down. There's no rotation on most joysticks, so there's no 1-to-1 comparison between the two.

I like my right x-axis to be strafing and my left x-axis to be turning, which makes turning while walking way more natural to me.

I think the article is right, and some of your explanation is post rationalization rather than actual reason.