Totally agree. I should add that in my experience, many AA agents' understanding of entry rules (be they passport/visa or health/covid) is less than perfect and I have had to patiently explain or demonstrate that there was no issue with my case more than once despite my situation typically being very mainstream. So in short, mistakes are not surprising in my view, and if the OP says that this is not the first time it occurred, I'd provide the family with a little printout of relevant rules in case to avoid future aggravation. By contrast, the whole idea that AA "was trying" to randomly get rid of pax due to overbooking strikes me as a bit of a non-starter and I'd forget that sort of conspiracy theory.