gentoo
I think the reason this could reasonably be called 'private' is because the pilot is not going to be making any money out of it. The record of payments will quite clearly show whether the costs were shared equally.
i don't think under the new rules the costs have to be shared equally
1.6 The EASA Air Operations Regulation was amended in 2014 to include some exceptions of its own, similar to some of the exceptions in the ANO. Two of these EASA exceptions go further than the ANO:
• the EASA exception allowing cost sharing permits up to 6 persons to share the cost with no minimum contribution and no restriction on advertising, and
3 Cost-Sharing by Private Persons
3.1 The maximum number of private persons who must share the direct costs (and only the direct costs) of the flight is increased from four to six (including the pilot), and the requirement for those costs to be shared equally and for the flight not to be published or advertised is removed.