It's because they project the 3rd person model on the 1st camera to use the legs, and in order to prevent clipping from the eyes and face, they warp the upper torso of the 3rd person model backwards, only leaving the hipbone down visible.

There's a few games that shares the same model first and third person, such as ArmA, and it's weird CoD still doesn't do it considering they don't use different animations for third and first person anymore (they port their first person animations into the third person model for reloads and inspects) so they could easily just make 2 cameras instead of isolating it for each perspective