Also, are airlines NOT required to book you on other airlines in the event of overbooking? So if one chooses to fly on another carrier they do so at their own expense?
As with any business, the airlines will mostly offer you first what is most advantageous to them, not you, that will still comply with the rules, until it starts getting expensive for them. If you know what the rules are, you may refuse their early offers and ask/negotiate for something better, hanging your absolute rights to compensation as a passenger over their head. There's nothing like an informed consumer.
For example, when I was overbooked with about 10 others for a United flight from LAX
when they ran every half hour, they began rebooking us not on the next flight out, but the one 2 hours out, claiming it would get us to our destination within the lowest rung of compensation.
After the first couple of people accepted this along with a free ticket anywhere in the U.S., the next person piped up and said, "If you can't confirm me on the 9:30, 10:00, or 10:30 flights, you owe me compensation for 4 flights, not one." Eventually they agreed, and all 10 of us cleaned house in compensation.
"No, the meek shall not inherit the earth, they don't want it."