Exactly. The ground is usually 58F. I remember reading about this in a thermal home book. (If you effectively bury 3/4 of your house, you only ever have to warm it to 70F from 58F.)
It's actually somewhat funny. Did they think there were ice cubes under the grass when the designed this?
AFAIK, the ground temperature will be the average air temperature over the year. It's certainly not 58F everywhere, because in Siberia there's permafrost, and in Denmark might likely be less than 58F, too.
Based on quick search, the average air temperature in Denmark is 8-9°C(46-48F)[1]. I suspect that you don't find that cold ground temperatures though. I found some local statistics about ground temperature[2], which shows that even around here the invention would barely work in the warmest months. And I'm living nearly thousand miles northwards from Denmark, from the same source the average air temperature here is -2°C.
I'm just giving this as more nordic perspective, seeing that most HNers probably are from US/warmer climate.
For the purposes of a just-below-the-surface cooler, yes I believe you are right. But my understanding from the book is that if you go slightly deeper, you will get to a somewhat universal soil temperature no matter where you actually are, with extreme counterexamples, I'm sure. The book, on thermal housing, may have been assuming habitable areas, not Antarctica or Siberia.
The 3rd post talks about the variation in temperatures. Seems that once you get to around 30 feet down the temperature becomes constant year round. For Houston the chart says 71 degrees. Because it's that single number instead of a range I assume that's the temp you get at 30 feet deep.
Otherwise, this is luddite technology designed to appeal to ecotards.