I was looking for such a cup about a year ago and someone suggested
Campmor as a source. I bought a couple of the "Olicamp Space Saver Cup" (item #25001, $5.99) and have been real happy with them. They are also made out of stainless steel. I've heard the "Snowpeak Titanium Folding Cup" (item #65123, $24.99) might also fit the bottom of a Nalgene bottle but I haven't seen one in a store to try it.
The website you mentioned is an interesting one. The collapsible tripod stove looks like something I might try. They show it used with Sierra cups but one of these "bottle cups" should work on them also. I think the fuel tablets from an Esbit stove would work or it could probably be set right on top of the coals from a wood fire. I already carry an Esbit stove but I'm always looking for something even simpler.
Terry