Now finally I can see what you called "the error in this" - it is in the diagram itself!
I didn't look at this carefully since I regard it as a symbolic picture. And this it is!
It's not a real diagram of angles and distances.
The scale is completely distorted!
In real life the distance tu Proxima Centauri is more than 100.000 times of the diameter of earth's circle round the sun.
So the diagram would have to show the star about 3 km (!) to the right.. Or earth's circle smaller than one single pixel. Both is obviously impossible, but the imagination may show you that you are right in regard to this poor diagram...