Maybe. I hold it so that the weight of the controller is balanced and resting in my palms, which puts it at something like a 55° angle.If you're pushing the stick "up" and "down", then I can only imagine that you're holding the controller at a very unusual angle.
If you have a DualShock 4 and balance it on a finger, that should give you an idea of what I mean.
Oh, I see. I thought you were controlling it like a camera operator would, where you push the tripod head left to pan right, and down to look up.With regards to X-axis, the logical corresponding input movement would be to twist the stick, which is impossible and would feel horrible anyway (not least because it would be pretty much impossible with one thumb alone). Tilting left and right to turn is the best compromise, but neither "Normal" nor "Inverted" in that case correspond to the camera movement (which would be to roll the camera).
Not that you hold the controller completely horizontal and imagine it's the camera itself, which doesn't make a lot of sense since you would be rolling the camera.
That seems like an arbitrary justification, and I would think it obvious why that is considered to be "inverted" rather than "normal".