If you watch this video, you will see that Slingshot is a distilling machine. The key to it's potential is that it is a very efficient distilling machine, recycling the heat given up by the condensing of steam to liquid water to pre-heat the incoming dirty water.
The Slingshot has no direct inter-relationship with Kamen's Stirling engine generator. Slingshot needs electrical power, and the Stirling generator can provide it, using non-conventional fuels and apparently quite efficiently, but it could get electrical power from anywhere else, if it were available.
Suppose one designed a still that operated directly on cow chips, but implemented some of the efficient insulation and heat recycling technologies? Perhaps not as tidy as the Slingshot, but no electrical power required.
However, Bob Kerns has an excellent point: Renewable fuel sources might be available, but that doesn't mean they are good for the environment. As an example, Colorado began setting limitations on wood-burning stoves and fireplaces years ago. Some of the beautiful ski-resort areas were getting overwhelmed with air pollution.