It's the Citizenship and Immigration Services. They document and regulate everything. The airlines are a pay for transportation publicly traded for profit enterprise. They wouldn't care if you were from Mars.
No it appears all automated. I know they have records of flight records and days spent out of the country. So, apparently when a LPR buys a international ticket the USCIS system does some sort of an eligibility check
airline employees don't unilaterally make decisions on who needs a re-entry visa and who doesn't. That is done exclusively by the USCIS IN America. Which appears to be the case here but in error
actually I got a formula from a 3 minute YouTube video by an Immigration Attorney and got right thru to a live body after numerous unsuccessful attempts and disconnects. It was crazy
I talked to CBD, and it's not their jurisdiction. This appears to have been put on by USCIS as a suspension or revocation of her Green Card in error as when I talked to the agent there was kind of an "OOPSIE" in his voice and it had been removed when I went to the airport.
Personally, I'm more drawn to "real Thailand", Ubon is one of my favorites on the Lao border west Thailand, or make it to Angor Watt in Cambodia. Island hopping is a tourist thing but it's not very culturally enlightening. Mostly day tourist. But that's me, as I grew up on an island