It's an active domestic non-profit corporation in Michigan. The Articles of Incorporation date from 1958. It looks like there are 2 classes of membership, "Regular" and "Sustaining". A sustaining member must be an owner of property in the OP's subdivision and be elected into membership by 2/3 of the members. A regular member is the same with the added proviso that he/she must also be a SHAREHOLDER in the association (the park assoicaiton, not the subdivision). Members get to use the lake subject to rules & regulations promulgated by the Board. Sustaining members - those who are not shareholders - have no voting rights. Regular members may transfer their membership but sustaining members may not.
So it looks like some subset of homeowners in the subdivision owns the 150 shares of the park association and get to control who else may use the property. Does this Park association actually hold title to the land in question? The Articles of Incorporation give it the power to purchase, own and manage land for recreational purposes so my guess would be 'yes'. The corporation continues to file annual reports.
MarkW, here is
where you can find information regarding the Articles of Association and the Annual Reports of the Park association.
It looks like the info you were given was accurate.