CW, but if you read the regs there are 2 parts on private ops. The first one, which Fission brought up, defines what a private op is. The second part, under the hdg "Private Operations" states that
(7A) An aircraft that carries persons on a flight, otherwise than in accordance with a fixed schedule between terminals, is employed in a private operation if:
(a) public notice of the flight has not been given by any form of public advertisement or announcement; and
(b) the number of persons on the flight, including the operating crew, does not exceed 6; and
(c) no payment is made for the services of the operating crew; and
(d) the persons on the flight, including the operating crew, share equally in the costs of the flight; and
(e) no payment is required for a person on the flight other than a payment under paragraph (d).
I'm personally inclined to think that this is just stating that this type can also be counted as private, however if someone knows a FOI perhaps they can give a definitive answer?