My understanding of the right to log P1/s (at least, in the UK) is that the pilot must be an ATPL holder, rated on type (or undergoing a successfully-flown type rating test), and handling the aircraft as well as making all decisions regarding how the aircraft is operated, whilst being under the supervision of the actual commander.
I see nothing fraudulent about this, since it is a recognised and accepted practice.
That having been said, the different capacities that can be entered in a logbook and how it is broken down in columns is a waste of time and is overdue for a radical overhaul.
IMHO P1/s should be flown from the left seat with a training captain in the right seat, e.g. on line training flights. I see no reason to break down logged hours into PF and PNF. In a multi-crew aircraft, everything should then be logged merely as P1 or P2.
There will always be oddities and anomalies, but I think the whole system needs more clarity, and the CAP407 logbooks also need redesigning. What, for example, is the difference between "Dual" and "P2"??