I'd like to add perspective as a former airline station manager. I last managed an airport location for my airline with almost 50 mainline flights a day and non-stop international flights to 3 non-US countries, plus of course connections to many more. We linked directly to the Timatic website rather than via an interface. Most system interfaces or copies of a database update on a cycle and not continuously. During COVID, some countries were changing requirements by the day or sometimes a couple times in a day (during part of the pandemic I oversaw another airport where we were next to Qatar Airlines and I could hear their shift briefings.... "What does an Uruguayan passport holder with a US green card need to transit Doha and end up in Iran with no proof of onward travel?"). Our kiosks and check in system were programmed with most transactions, especially the 75% ones... like a US passport going to Mexico or Jamaica, and even if the customer put this information in when booking, it would run that DOCS OK check behind the scenes and the agent just had to verify they actually had their passport. It's where visas, items inserted in passports, etc., are involved that it gets confusing sometimes.

Having 20 years of experience, and a master's degree to boot, I sometimes look at Timatic and have to shake my head and re-read it a few times. There is a song by the band Vampire Weekend called "Oxford Comma" where the first line is "Who gives a f** about an Oxford comma?" Well Timatic sure does.

US CBP has a sort of help desk, but to be honest they aren't overly helpful if they think you could have figured it out on your own. I was fortunate at my airport to have an outstanding CBP Port Director and her deputies were great and took the approach that if we asked for help or to interpret something, they'd help us because: 1.) if we sent an inadmissible, it was coming back to them, and 2.) at least half those inadmissibles didn't possess proper documents to re-enter the US (like a Visa not allowing reentry) so they saw it as heading off their own problem.

Training is done but it is hard to cover every eventuality. It's basically learning from experience with Timatic. And keep in mind you my face an agent, like most of mine, who didn't have a passport themselves and many of them had never heard of a visa before outside of the credit card. One day I was asked "Jordan? Like the ramp supervisor Jordan?" The high school state geography bee 1st place winner in me died a little that day. But, it is what it is, and as mentioned in this thread, getting a supervisor involved is key. And yes, sending an inadmissible is a career limiting move and in some cases did result in immediate termination when fines between both the US and the other nation could total easily $10,000 plus we had to buy a last minute plane ticket from like Lima to Beijing to send the inadmissible to their home nation since they couldn't come back to the US for visa reasons.

Having a print-off of the rules for your situation I think is helpful. It is not going to convince an agent on its own, but may help guide them where to look to verify, so I thank the person who mentioned that they come prepared with that.