This is one flight out of thousands of US flights that flew on that day. So as far as I can tell it comes down to the fact that as the family had paid for the seat for the 18 year old son they thought it would be ok to put the child seat in that seat. It wasn't.
Having lived in the US we have travelled on many internal flights. Never have we seen any one being thrown off a flight or had any trouble ourselves. The number of flights that we have been on where they have asked for volunteers to fly later can be counted on one hand and never has there not been enough volunteers.
We have used Delta(80%), United, Jet Blue, South West and Virgin internally, all with no problems. Follow a few simple rules, check in on line (most Americans don't), get to the airport in good time, don't think that the rules don't really apply to you and finally check in a bag. I know it can cost more but they don't like the hassle of trying to find your bag if they want to bump you off.