wait, how do you play with inverted mouse? what controller do you use? a touchpad?
The way I could try to make sense of it is, something is being moved from outside so pushing the mouse forward means look down. Flight sims, joystick, 2d plane, ...stuff.
If you were holding a gun with two hands (and you're right-handed), you'd lift your right hand up to aim down.
By that reasoning pushing the mouse right should rotate the view left.