Just a thought that came to me, was wondering what would happen in this hyperthetical situation.
I understand that PC precepts are collected at the same time as your council tax (for efficiency reasons), but are not actually part of the council tax. If you don't pay your council tax the big council has powers to make you pay this.
If you council tax was £1,000 and your PC precept £20, but you paid only £1,000 (and made it clear you were paying the council tax and not the precept), who's responsibility would it be to chase that £20 debt? Is it still the big councils job?, would the PC have to do it?, and do they have any powers above what anyone else has in relation to unpaid debts?