No stira. The map is to inform you which merchants have a physical location. A merchant may have a physical location, be on the map, and be ineligible for other reasons (eg nonprofit etc.)
Nowhere in the terms does it say that all those on the map are eligible.
The Small Business Saturday Map is an interactive map created to help Card Members find and shop at small businesses. It is also a resource for Card Members to find a qualifying small business location where they can redeem the American Express Card Member Offer for Small Business Saturday on 11/30/13. The Small Business Saturday Map will be available to Card Members from 11/21/13-12/1/13. Online-only businesses and businesses without a physical storefront or location do not qualify to be included.
The Shop Small Map is an interactive map, available throughout the year (except from 11/21/13-12/1/13 when the Small Business Saturday Map is available), to help Card Members find and shop at small businesses. In addition to displaying merchants with a physical storefront, the Shop Small Map also displays merchants that only accept online transactions or those that do not have a physical business location. Merchants that only accept online transactions or those that do not have a physical business location will appear on the Shop Small Map until after Small Business Saturday, Nov 30, provided that they are eligible.
How do I know that a particular small business location in my area is a qualifying location?
Of course the fact that it’s on the map doesn’t mean that the business was truthful in their application, but the FAQ seems to indicate that the consumer is not responsible to make that determination.