APIS is there so the information can be passed on to the arrival/transit country, it doesn't serve as a way of the airline reservation system alerting you to the entry requirements.
There are so many combinations of passports, visas, residency cards, special cases (I've seen some countries allow visa free entry to certain passports provided they were flying on certain airlines) a person could have, it would be impossible for a computer system to simply say yes or no to everyone, which is why a document check takes place at check in and agents make use of TIMATIC. Even TIMATIC can be confusing or misleading so more often than not the best thing to do is for the airline to call the people at the other end and let them make a decision. This is what happened in your case.
Do you have reason to believe they didn't call KEF and simply denied you? I doubt the groundstaff would do that to be honest.
It's a situation I saw countless times when I was a check in agent. The final decision rested with immigration at the other end. I'm sorry to say that US passport holders were among the most frequent people we had to deny travel to because they didn't meet the entry requirements of the destination. I saw plenty of people (US and otherwise) being turned away for even just a day trip because of the validity problem.
It's not so much that your pleading fell on deaf ears, but they were simply denied, by Iceland, from letting your wife board their plane. An airline faces a huge fine, mandatory carriage of the person back to the origin (which could be at the expense of another confirmed passenger being offloaded to make space and any time in between landing and removal will usually see the passenger detained or if they are allowed in they won't get their intended time in the country) and, in extreme cases where they become a persistent offender, and airline can lose the right to fly to the destination, although if that's actually ever happened, I don't know.