Almost no credit card insurance is applicable in Japan, so you better call Amex and verify your coverage - regardless of who you rent from, local "LDW" is pretty much compulsory and is often built into the rate that you are quoted. For liability purposes, they may offer additional protection above the mandatory base built into the rate - you can decline the extra, but it has nothing to do with damage to the car, nor does Amex include liability protection either way.