G'day NotaLOT,
As I understand it, protected areas should be obstacle free in case the aircraft is not able to stay exactly on track - i.e. it offers a buffer of space that the aircraft will to a high probability always fit inside when flying the procedure.
Yes this is correct.
The protections areas are based on an idea of aircraft containment, and take into account system accuracies. To this end the areas sepcified in PANS-OPS are designed around 3 standard deviations, or 99.7% containment. Have a look at PANS-OPS Vol2 Part1 Section2 Ch2 Para 2.8 for ground based navaids.
Also have a look at Part 3 Section 1 Ch2 for RNAV info.
Hope this answers your question
Alpha