Similar happened to me. Here's how they operate. They scan public records for any significant changes. In my case, I got remarried a year ago. I got a bill from Verizon that was $20.00 higher than normal. When I investigated, the additional charges were from Enhanced Long Distance. I called and they claimed that they made arrangements with my wife for the service.
The reason I know they got her name from public records? Her name was severely misspelled on our marriage license. If anyone calls and uses the misspelled name, she goes nuts.
Something similar may have happened with your grandmother. A move, selling apiece of property, etc will result in a new public record and provide Enhanced Long Distance with an opportunity to create a new account for you.