So just to clarify are you saying that if you report 15 minutes early that you would make this your FDP start time? If the FO had reported 30 minutes early would you make that his report time?
Yes and no. The law in my country states flights have to be planned in sufficient time including the preflight preparation. So by law, a company must plan your roster, and thus your FDP, to include the time you actually need to do your briefings. I assume it is not different in most European countries.
So yes, if the time given is always too short, I do believe if you report early, it should count. The time they do give is counted. If you report early without any need since the standard time is sufficient for most of the flights, it is your own choice.
FDP is defined as a period in which you are required to do work for your company. Showing up 15 minutes early to make enough time to do your work seems to me to fall under that definition.