Hi vilas,
Basically it was named so as to identify the beginning of the ILS approach so you can legally continue to minima even if weather goes below minima.
I do not see the correlation between the FAP and the wx deterioration below minima. You can start and continue any kind of approach until the OM/equivalent point/1000 ft AAL regardless of the weather conditions. You need to have the minima by the above mentioned point at the latest to continue down to your minima.