"This matches observation" is a random phrase. Do you remember what saying random phrases does not cause? C'mon, boy, I know you can do it!
"Yes, on the equinoxes, the illuminated area is a semicircle with the terminator halfway around the disc from the Sun. In June Solstice the illuminated area includes everywhere north of the Arctic Circle throughout the day, but nowhere south of the Antarctic Circle anytime during the day. In the December Solstice, the Sun's illumination includes everywhere south of the Antarctic Circle all day and nowhere north of the Arctic Circle any time during the day.
For the observer south of the Antarctic Circle at midnight on the December Solstice, the Sun appears due south, even though the shortest distance to the Sun would be to the north across the darkness at the North Pole." - An interesting claim. Where's the support?