The rule for Schengen Countries is that a pax goes through immigration and customs on first arrival in the first Schengen Country,and then only goes through Emigration on departure from the last Schengen Country
That isn't right for through tickets as far as customs for checked baggage goes. If bags are checked through, they go to the final destination, and customs officers could be standing by wanting to inspect bags that don't have a green stripe on the tag. Apparently for this questioner, the bags won't be checked through because of AA policy, not because of Schengen rules.