The guy is technically wrong, but the FA does a horrible job explaining it and starts making up way too many (completely false) excuses that she can't then dig herself out of.

Now some genius Congress is going to get some hairbrained idea that all airline tickets must be fully transferable and refundable at all times, combined with no overbooking. That sounds wonderful up until you realize who will end up paying for that new setup...

Credit where it's due, the guy kept pretty calm and collected in what was certainly a tough situation for him and his family, and relatively quickly made choices to take care of them in the moment and then deal with DL's decisions later.