But, given a fixed dev time, it's best to build a website that can handle most customers needs, and then give customer service (via phone/email) the admin/power user abilities to deal with the few special cases that the website cannot handle.
So, IMO, the airline here has done everything right.
It's great that admins can fix the special cases, but the fact that they're special cases at all makes life harder for assumption-breakers. An action that took 10 minutes on the Web for Jim Smith living at 11 Place Road might be 3 hours on the phone for Hector Marίa Gonzalez López whose address is a P.O. box. Those hours add up and can really make folks' life hard for no good reason.
Do your users a favor and make as few assumptions about them as possible!
They haven't done anything harmful on purpose. Also, they provide an alternative path (calling their customer service) that works.
During the last decades, companies and government services have reduced human agents as much as possible to reduce costs. However, this type of problem highlights the need to provide an alternative path. A silly bug or requirement omission may harm many people when there is no alternative.
Anectodal example: I live in Argentina, and my father is an accountant. I've heard him say that many times, the systems provided by the AFIP (the equivalent of the IRS in the US) don't allow certain situations allowed by the tax laws. He often says that a bunch of uninformed software developers are doing whatever they want with the Constitution. I cannot stop thinking about our responsibility as software makers.
But really, how can you argue with a computer? Sue the IRS equivalent?
This is why regulations and standards imposed externally exist. Notably accessibility requirements.
Typically, the problem here is that customer service is unwilling to deal with these special cases, through some combination of:
1. They are too scared to correct the data - e.g. they have been told to follow some poorly-thought-out procedure to the dot and/or they're scared of committing some sort of "fraud" by entering the data sensibly.
2. Although they could handle such cases in their system, the system has to interface with a labyrinth of other systems that can't.
3. They have to use an interface that is essentially the same as the website, with all of its limitations.
Ie. They write a note saying 'let OP onto the plane, their seat is 1A', then mail it to OP.
As far as the system is concerned, OP's ticket may not exist, payment may not exist, flight may not exist, etc. but the note from customer service is enough to get them to their destination.