You had it right. Remanufactured ammo goes through the same, large scale process as factory ammo except with used brass.

The owner of the range I used to work at (one of three locations) also owned a company that produced remanufactured ammo. We'd send the brass off the range to get recycled and then sold it when it came back all ready to go. He even guaranteed the ammo just like the big guys if it directly damaged a gun. That guy was a genius.