I think good ol' Joe may be splitting hairs a bit.
The yeti technically isn't situated in the "mountain" part of the structure, but just inside the rear "warehouse" area. He is not surrounded by mountain structure at all. This is always confusing for people. The rockwork doesn't go all the way around.
However, the room where he is located is heavily themed with rockwork. No doubt some of that work had to be completed after the animatronic was installed. Perhaps that is what he was talking about.
As for the TV shows, look on youtube at the Discovery channel show. They clearly show, near the end, the yeti being shipped to AK and installed in the room inside the structure. The room is already filled with rock work while they are installing him. Joe has to be referring to doing some finish work on the indoor rockwork.