Indeed, motion blurring preserves almost all* information of a picture, given some assumptions (e.g. brightness stays constant, path is predictable).
*A linear blur of a 2D picture acts like a 1D sinc filter: information is completely lost only at spatial frequencies multiples of 1/d in the direction of motion, where d is the linear displacement, and otherwise attenuated.
*A linear blur of a 2D picture acts like a 1D sinc filter: information is completely lost only at spatial frequencies multiples of 1/d in the direction of motion, where d is the linear displacement, and otherwise attenuated.