If you rent in Australia, New Zealand, Italy, AMEX excludes those countries while Visa would pay the excess as these countries, AND Costa Rica according to Chase, have government mandatory basic insurance built in the rental rate. However the excess (deductible in US terminology) is high like several thousands dollars. Visa covers those. The 2nd rep I talked to is quite knowledgeable and seems to be well-versed in those situations as she correctly uses the term "excess".

The strange part of the AMEX Premium is, we enrolled husband's SPG card. It did charge us $19.95 for our rental in Hawaii in March this year, as well as our rental in San Diego in Dec last year. Yet, it never charges us for a 9 days rental in France this May. I even called ahead of the trip to get the claim telephone number should we need it and got the collect call number, as well as the number in France.