So let’s blame the customer because we use an antiquated system and make sure to show no sympathy.
I didn't say blame the customer, I say blame this agency.
Yes I have full sympathy with this person. I had a while back a cleint in this situation and was traveling from the US via Canada to TLV, and they call me from the airport that they are not a US citizen and therefore require a ETA for Transit and till they got it done it was too late and the airline doesn't want to wait. I had to plead with check in agent over the phone (a miracle the agent even wanted to talk with someone) and he said it's my issue etc - I begged him and explained and as they had no luggage he agreed and they got a supervisor to speed them thru security. The flight left pretty much on time nonetheless.
Yes, United should have showed sympathy, after they removed her they should have kept the plane waiting a few minutes and give the women an option to buy a new ticket, but in this industry sadly this is too much to ask. See when it does happen it makes national news that a pilot waited