Delta owes an apology for some incorrect statements and for being rude. But that does not mean that they were wrong about that status of that seat. The dad was wrong. If he had bought the baby a seat he would have had no problems.
I will give you that the story was not long on facts, so I may not have all the true info. But it sounds to me like the Dad *did* buy the seat. Your gripe, and Delta’s (maybe the same? Do you work for Delta PR?) seems to be the name of the person *in* the seat.
Rude? They blew past “rude” at roughly the speed of a cruising 757 when they told a mom she would be jailed and her kids would be taken away. They can apologize until blue in the face and they won’t be able to back that truck back up to “rude”. Sorry.