Since I don't have a video or picture, I'll try to do my best.
I am using Invector Shooter and the reticle always remains in the center of the screen no matter how my gun moves. When I am in "Aiming", the gun points to the reticle however if I stay in the Aiming state and start walking, my character bends a little to mimic walking. The gun points down now, just a little, but the reticle doesn't.
This is a bigger problem when Aiming and crouching. My gun points up slightly but my aim appears to be aiming down. So it appears as if the bullets are magically shooting down.
This doesn't appear to be an issue in the demo scenes but the body doesn't move during walking and somehow remains consistent when crouching.
I don't care if my players body bends or not, just looking for a way to solve this, especially for crouching.
I messed around with the camera as you said and that helped a lot with the crouching. But when player is standing and moves - that's my issue. Watch as the player is aiming, then move left, right, forward. The gun points down, away from the reticle. I wouldn't mind even if I could keep the player still.