The Sea
The pdf link is merely a report into subpart q versus CAP 371. Makes some valid points but it's not a working document.
I found what i was looking for and would suggest that in depth read of your company FTL scheme will facilitate an answer.
As to why an augmented crew may increase the allowable FDP is a rule that the authority has imposed and we with our Crew Scheduling caps on merely abide by the rule.
I would suggest however that if you want to know why then ask your CAA directly as i'm sure they will be only too willing to help.