I don't know what state you're in, but in California, voter registration does not have to be done by state or county officials, as you said. Most voter registration is done by volunteers, standing outside stores as the woman you wrote about did, or by people at swap meets or town festivals and places like that. Is it illegal to register voters outside stores in your area, or was the woman inside the store?
Yeah she was inside. According to a website that was posted these are the locations that are valid:
County Clerk's office
Board of Election's office
City and village offices
Township offices
Precinct Committeemen
Some schools
Some public libraries
Some labor groups
Some civic groups
Some corporations
Military recruitment offices
When applying for services at the following:
Driver's License Facilities
Department of Public Aid offices
Department of Public Health offices
Department of Mental Health & Developmental Disabilities offices
Department of Rehabilitation Services offices
http://www.elections.state.il.us/VoteInfo/pages/Register.htm