From: Washington, DC
I've read about this policy in other publications and want to mention two factors which provide additional context:
1) As Amazon has been rolling out same day delivery, for business reasons it focused on more densely-populated, high income areas. As a result, the service was not available in many low income areas, and so the company was accused of racism. This program is probably in part a reaction to such criticism.
2) It is well documented that many low-income areas are "food deserts", or more accurately "retail deserts"--in other words, there are no real supermarkets or other retail outlets for neighborhood residents to shop--only fast food, convenience stores, etc. Therefore, especially as Amazon expands into grocery delivery, Prime could offer a real service to these residents--and a real market for Amazon--if the residents can afford the membership fee.