I would not have thought of this as a major issue unless Evers and Laville (2004) The third sector in Europe, Edward Elgar, spesifically discuss whether cooperations are defined within or outside the third sector.
The characterisation of third sector governance is too crude. For example, the third sector itself can be seen as diverse with philanthropic, mutual, cooperative and association sub-sectors. The comments at the start of the literature review might apply to foundations and charities, but are less true of association and mutuals (let alone cooperatives). Also, where there are accounting regulations (like SORP), there are mechanism that keep associations and charities accountable to their donors.