This is where the confusion is and we need to understand what happened exactly. Even if I buy a ticket for a flight, but I don't go into the airport and check in for the flight at some point the airline is going to put someone else in my spot when I haven't checked in. The 18 year old appears to have never checked in to the flight so they see a no show and at that point they put in a standby passenger.
The article is fucking crystal clear. The 2 year old wasn't allowed to fly in a seat that was reserved under the their 18 yr old son's name. This is an absolutely ridiculous adhering to the 'letter of the law' instead of the spirit of the law.
And seriously, fuck whomever threatened to jail the parents and lose the kids, seriously what the fuck is wrong with that person and have they been suspended (or fired) yet? At worst, the family made a clerical error.
If it was me, I would have bluffed and told them to unboard my two year old. That I'd order a ticket for the child once on the ground in California and they could fly back. This could have potentially put Delta on the defensive, telling me that I can't leave the child at the airport. "I'm complying with your instructions that they can't fly."