The photographer said he used the flash as fill - the girl's body caught the majority of the light from the flash and "fixed" her on the image. The mic cord, OTOH, because of it's size and color, would reflect back virutally none of the light from the flash, so it's image won't be fixed. It's lighting would come from the rest of the light in the room and it's movements will show up as a blur.
Another point that helps verify the photographer's claim - the narrow depth of field, which is the amount of the frame ahead of and behind the lens' point of focus that will be relatively sharp and in focus. You get shallow depth of field when a lens' aperture is wide open (i.e. at a low f-stop number), which you would do in poor lighting so you could use as fast a shutter speed as possible and reduce blurring.
There's nothing fake going on here - this photo is an example of trying to find the right combination of compromises to get an acceptable result in adverse conditions. I actually think he did a rather good job of it. It's hardly world class, but he did a lot better getting the shot than I probably would have.
Thanks for the explanations. For all I know, it could have happened that way.