The stabilised approach criteria in my current airline specifically excludes PAPI from the definition in order to allow for approaches not coincident with the PAPI slope.
A case in point is the RWY05 VOR/DME approach at Geneva, which due to terrain is quite a bit higher than the ILS & PAPI. On the VOR/DME correct profile, at the minima, you will have 4 whites on the PAPI - but under our definition this is "stable" and you may continue to a landing.
Interesting about the USA FAA rule regarding touch-down zone. In Australia the company had an SOP about the touch-down zone, but my UK airline seems to ignore it completely in their manuals and operation. A mistake IMHO.