The car was commissioned by the family that founded Fiat, the Agnelli family. They also had the largest holdings on the Italian stock exchange. They owned a remarkable French villa, one famous for once having been owned by kings, and entered the car in the 1957 Paris auto show... and I guess that is where the Cord and Doheny family saw it and bought it, because they had it at their vacation resort, Lake Arrowhead California by 1959.
The special 600 was called the "Eden Roc" as the promontory overlooking Cap d'Antibes along the coastline of Cote d'Azur where the Villa Leopolda is, in the town of Villefranche-sur-Mer. The little Fiat was used to shuttle guests around the 20-acre villa and town.
In the late '60s, this car was taken to the Lingotto in Turin and replaced the Fiat 1900 Cabriolet Boano used by Prof. Valletta to lead guests to visit the factory. http://www.alfabb.com/bb/forums/other-italian-cars/160958-funny-fiat.html
The French resort was Villa Leopolda, owned by King Leopold of Belgium, and King Albert after him. It was used in the Hitchcock movie "To Catch A aThief" that starred grace Kelly, later Princess of Monaco.
Most recently, according to Wikipedia, it's owned by the Russian billionaire, and he bought it for the world record price of 370 Euro http://en.wikipedia.org/wiki/Villa_Leopolda