Instead of a regular card-reader that scans a card, this scans as many items of personally identifiable material as feasible (at least 10 fingerprints and/or a retinal scan, maybe a pulse check), stores a hash of the above in a central db to prevent abuse, and only authorizes the vendor to dispense a dollar for unique metrics captured. The physical 'dollar' actually comes from the store/business till using the local currency, and the business then invoices you seperately for every dollar they gave out.
The cost of the terminals would probably come from the millions that you wouldn't be able to send a dollar to anyway, like you said terrorism or other concerns.