The general principle at work here is that if an unsuspecting member of the public pays for a flight in an aircraft, they have the right to expect that aircraft, crew and facilities are of the high standards expected for public transport flights.
There are some exceptions made, including the charity exemptions in the AIC, and the cost-sharing provisions for a PPL. The assumption there would seem to be that a consenting adult chipping in to cover only the costs of the flight knows what he or she is getting into. But any payment over and above that (or even instead of that, as might be the case for a charity flight beyond the exemptions) makes it public transport.