In regards to the kickstarter, even with this small of a system with a small fish, I'd still imagine they don't have
enough rocks to provide enough surface area for the proper bacteria culture to be able to keep the
water completely clean, but may extend times between cleaning, or like many people I know you can also use the tank water to water other plants and top off the tank. Normally in other systems I've looked into the grow beds are much larger then the tanks themselves.
I had a similar small system and although I used a gold fish and they tend to be messier then bettas, it quickly surpassed the cleaning capabilities of the gravel. Resulting in the Missus finding a dead fish. But then again might have went better if I warmed up the system. I'd recommend at least when first getting started to still run through a fish filter. I understand you need to build up the bacteria, the convert the fish by products into plant food, and the filter could help keep it clean while the gravel builds up that stuff.