AMEX charges a higher rate, so the places that don't accept AMEX tend to be the same kind of places you'd not want to shop at if is possible. This includes some off-brand gas stations, corner stores and thrift/goodwill/dollar stores.Um, so which one is it? I highly doubt the guy who posted the 1st quote is correct... I'm sure more places accept AMEX cards than you think.
That said, these are far and few between, and generally reflective of the community of the store's location. Many asian grocery stores tend to do everything possible to get you to pay in cash.