Was the requirement for a visa wrong? It may depend on the passport, but as the end of the journey was in Switzerland, was a Schengen visa required for them?

If they were then denied boarding compensation might be due, but it depends on the details. From your itinerary it seems you started in Mexico so was that where the problem arose, I am assuming that is an AA flight to DFW and it was AA agents dealing with them?

I am just trying to check if it is clear the denial was incorrect, who actual did it, and where.