I know its a bit "does it really matter" but I like to understand the small things as much as I can lol.
As for a FAF being a defined point and a precision approach doesn't have a defined point...it does have a defined point, and can not differ on the same approach. The defined point is where the intermediate approach segment intercepts the minimum glide slope intercept altitude, that can only occur at one particular point, and it need not be a named point. For example look at this approach:
http://www.myairplane.com/databases/.../00651IL16.PDF
Although the lightning bold exists at a different point than the cross, and the lightning bolt does not have a name, according to the FAA it still meets the requirements for the FAF: It is where the final approach segment begins on the precision approach, it is also a FIX according to the FAA, it is a geographic point in reference to another navigational aid. It can only occur once over the surface of the earth.
As for the lighting bolt, according to the FAA's definition, it defines the FAF not the FAP:
FINAL APPROACH FIX- The fix from which the final approach (IFR) to an airport is executed and which identifies the beginning of the final approach segment. It is designated on Government charts by the Maltese Cross symbol for nonprecision approaches and the lightning bolt symbol for precision approaches; or when ATC directs a lower-than-published glideslope/path intercept altitude, it is the resultant actual point of the glideslope/path intercept.
EDIT: by the way, I am not disputing that the FAP does exist, it does exist, however according to the FAA's definition it is called a FAF. The FAA defines FAP as when a NPA does not have a FAF.
Again, I know its a "does it really matter?", but to me it does :-) Just want to understand some of the
intricacies.