As I understand the process, its not really a function of the machine to be able to print the thickness (thinness) you want, but rather the slicing software used to produce what is called G-code, to drive the printer.
If you were to draw a plain cube or open topped cube in a cad program, Sketchup for example, that software does not define the open topped cube as a solid as it is not "water tight." The cube however is.
When the cube is brought over to the slicer software, (cura, Simplify 3d, etc...) you can tell it how thick you want the walls and how much infill you want. So if I wanted a really thin walled cube, I would set the wall thickness to a ratio of the nozzle diameter of my printer, and 0% infill. This could produce what you are after, but it all starts with the design software first. If you don't have a watertight model to begin with, the slicer software will have a fit because it is not programmed to deal with such things that essentially have no mass and take up no space.
I believe the house printing machines essentially are set up to follow a path much more like a laser cutter does rather than a printer. The thickness is more determined by the concrete output rather than the software driving the "print head."