Beautiful animations, I had seen them a few weeks ago.
About accuracy, and besides how cool the video is, I think it's simply a matter of point of reference. If your reference point is in the middle of the galaxy, the solar system will appear to move as a vortex. If it's in the sun, the planets orbit it. If it's in the Earth, you will have a complicated mess of spheres as in the Ptolemaic system.
The models are relative, but some might be more effective or simple than others when it comes to make predictions. Take for instance Copernicus. He describes an heliocentric model which is simpler and more precise than the geocentric in order to describe planetary orbits, then we consider this model more useful. I didn't find information about observations made with this helical model, and if anything would make it useful (and hence more accurate) beyond the visual neatness would be a prediction and a confirmation.
"The Menu is Not The Meal." - Alan Watts