Proxima Centauri's planet and the hazards of cool animations

It was officially announced today that Proxima Centauri has a potentially earthlike planet.  That's great, especially for fans of science fiction.  Here is a relevant video by Nature:

Did you spot the mistake?  The scientists discovered the planet by seeing the wobble in the star's motion (measured by painstaking spectroscopy of the starlight, and using the Doppler shift of the spectrum to "see" the tiny motion of the star).  The animation tries to show this at 0:55-1:12.  The wobble is because the star and planet actually orbit around a common center of mass located on the line between them.  Instead, the video seems to show the center of mass of the star+planet tracing out a circle around empty space.  Whoops.   Someone should've caught that.  Still an impressive result.

Update:  The makers of the video have updated with a link to a more accurate animation of the Doppler approach:  https://youtu.be/B-oZYm3L1JE.