the angles are really only there to illustrate that the apparent horizontal distance between the objects changed, which indicates to me, that the horizontal position of the person taking the photo, changed.
Like I said, create a model. It doesn't have to be exact. The only requirements are:
1. Take a photo of either the zoomed in or zoomed out position.
2. Without moving anything, other than the camera, take the other photo.
3. Make sure your results are the same as the Apollo shots.
4. Laugh at me for being wrong!
Seriously, I don't mind being wrong as long as it is proven. If you can do it, I'll need instructions to confirm your results.