They set up a sphere in a lab and turned on a light source and photographed the experiment. So it is a simulation of what we see in the many photos of the Moon posted on this thread and elsewhere. It duplicates the manner in which a celestial object like the Moon reflects the light of the Sun.
Of course it is coincidence that Moon and Sun appear to be of similar angular diameters as seen from Earth. Actually the apparent sizes are not exact. Sometimes the Moon is smaller and sometimes it is larger than the Sun.Is the fact that the Sun disk and the Moon are of the same size when viewed from the Earth, a coincidence, or a part of a cosmic intelligent design?
There are only two planets that do not have natural satellites - Mercury and Venus. All of the other planets have one or more moons. The angular diameters of all those moons as seen from the surface of their primary span a wide range of ratios compared to the Sun. The only logical conclusion that can be drawn is that there is no relationship between the angular diameters of satellites and the Sun as seen from any particular planet.
It is obvious to me that you are not going to be convinced by any evidence presented. So, we should not try to confuse you with facts as your preconceived presumptions have compromised your objectivity. It is reminiscent of the incident when Galileo showed his critics that Io, Europa, Ganymede, and Calisto were orbiting Jupiter, in a mini solar system. The critics looked through the telescope and saw nothing of the sort!
To paraphrase Philip K. Dick,
Reality is that which when you fail to believe in it, does not go away.