Yesterday was wash day again and I decided to try one last experiment. This time I turned all the underwear inside-out before putting them in the washing machine. The final count: 10 inside-out and 3 right-side out. After the dryer, the count only changed by one: 9 to 4.
Obviously, the washing machine does something to keep or turn underwear inside-out. My working hypothesis is that it has something to do with the seams on the inside of the underwear. However, I am not planning on exploring this phenomenon any further!