Oh no they didn’t.
http://www.gizmag.com/mushroom-tiny-house/28248/
“The mushroom part of the Mushroom Tiny House mostly refers to its insulation, which is based on mycelium (or mushroom root). This insulation is inserted between standard wooden panels, and is both fire resistant and green, containing no harmful toxins (unlike, say, Styrofoam). The company explained via email that the pint-sized dwelling also contains acoustic tiles made with the mushroom-based material.”
[edited post to make the link active]
That is wild. I’d be interested in seeing more on that. How very curious!