Where does the final approach begin if the glide slope is intercepted at an altitude above that depicted on the approach chart? The final approach segment for an approach with vertical guidance or a
  precision approach begins where the glideslope/glidepath intercepts
  the minimum glideslope/glipdepath intercept altitude shown on the
  approach chart. If ATC authorizes a lower intercept altitude, the
  final approach segment begins upon glideslope/glidepath interception
  at that altitude.


(FAA IPH, p. 4-53)

Does this paragraph imply that the FAF(FAP) for a precision approach fix (point) begins at the minimum glideslope intercept altitude when you have intercepted the glideslope at an altitude above that?

I always have thought the FAF for a precision approach begins wherever the glideslope is intercepted regardless of a glideslope interception altitude. Have I been getting it wrong all this time?

This question doesn't answer what I'm asking. I'm not asking where the FAF generally begins on a precision approach; I know where it begins and I've cited it above. My question is whether the FAF begins at the interception point even when the glide slope is intercepted at an altitude above the minimum interception altitude on the chart. The definition above from the IPH clearly says the final approach fix is the interception altitude when it's intercepted at an altitude below the minimum interception altitude but is silent on where the FAF begins if it's intercepted at an altitude above the minimum interception altitude.
The FAS begins when you've intercepted the GS, and are at or beyond (below) the charted GS intercept point (altitude).  So if your charted GS intercept is at BONGO at 3000' and you intercept the GS outside BONGO at 4000', your FAS begins at BONGO.  If ATC has you join the localizer at 2500' and you intercept the GS at 2500' inside of BONGO, then that point, where you intercepted the GS, is where the FAS starts on that approach that day for you.

There can be lots of ways to say that, some of which are less clear than others.  But that's the simple, and hopefully clear, answer.  And, maybe, going back to the FAA definition, you can see how what they put on paper matches this concept as stated here.