I've been running for a couple of weeks now with a full-size spare with no TPMS on my left front. The originally mounted tire/wheel with TPMS is stored in the back of the car, behind the drivers seat. That non-spinning TPMS tire/wheel is at 35 psi (it doesn't leak - I'm just adding the spare into my tire rotation). My TPMS light hasn't gone out since I made the switch. It stays on whether the car is moving or not. So along with malraux' quote from the service manual, I can confirm that a non-spinning wheel isn't detected. I have also read in other threads that some TPMS systems don't require the wheels to be turning, so maybe that's what your friends have?

I'm just using a very thin, stiff piece of cardboard to block the TPMS light. The cardboard slides behind the bezel around the gas gauge which wedges it in place.