For those of you who are curious how this terrible stuff is made I had the chance to take apart one of the cartridges. It is sort of like a toner cartridge for a printer with a little tube at the end and a chip that is read by the machine.
Above is the box. The box is open only on one end so water is not provided from the top to flow through. It seems that this little tube injects the sludge (i would guess simply coffee concentrate) into the hot water provided by the water input.