The trope that "German's Fled to Latin America after the war" is overinflated anti-Latin American propaganda at this point. The US and broader west took in just as many if not more Germans who fled.
I think it also has to do with the Schengen deal and making it easier for Latin American tourists to visit Spain and Portugal, as well as Rome which is a highly regarded tourism location for Catholics.
I think the same map mostly applies to all other EU countries, though your max stay is 3 months with no permits.