I recently watched Adorama's video on rear curtain sync flash photography. At 4.12 to 4.42, the presenter claims that when using front-curtain sync, the background/long exposure blur will be put on top of the frozen object, while when using rear-curtain sync the frozen object will be put on top of the blur.
I was under the impression that the sensors captured light in an additive way, i.e. the final image is a representation of the sum of all light that was exposed to the sensor, but then it wouldn't make any difference if the frozen object was exposed before or after the background blur.
Is there some kind of non-linear behavior of the sensor's recording that would justify what is being told in the clip above, or is this just plain wrong?