One other thing that hasn't gone mentioned here is that the family in the original article says they "just want their money back." It seems like a simple thing, but one hard and fast truth I've learned about travel is this: even in the absolute worst-case scenario when one party royally screws up inexcusably, Company A (Delta, in this case) will NEVER refund what was paid to Company B (NCL, in this case.) I follow a popular travel/consumer advocate and troubleshooter, and I have yet to see a case where one company has refunded money paid to another company. And there have been numerous stories similar to the OP.
At the end of the day, this is a cautionary tale for would-be travelers. We're conditioned to assume things will play out the way they're supposed to. If the ship sales at 4:30, a flight landing at noon should be fine, right? And the truth is, more often than not things run on schedule. But sometimes they don't. And that "sometimes" can be 20-30% of the time. I feel bad for the family in the article, but I saw three distinct spots where they could have been "made whole" but fell short.
The first was when they failed to purchase trip insurance.
The second was in booking their flights: it doesn't sound like they gave themselves enough of a buffer.
The third was in failing to procure passports for the family.
Basically, they set themselves up so that the only way things could have gone smoothly was if absolutely nothing went wrong. They opted not to use several options (which admittedly had an associated cost) which would have given Delta and/or NCL the ability to make them whole again. If you don't have a passport, you're not flying internationally. Period. If you're flying in the day of the cruise, you're basically only giving the airline a very narrow window to make up for any delays - and it might be sunny and beautiful between Atlanta and Florida, but if they're waiting on a plane from New York when there's a blizzard going on, that delay is going to be unavoidable.