Not a lawyer, yet have experience designing and developing land from both the developer and government side.
I don't know the MI laws, yet there is a good chance the lands in question are considered quasi governmental as it is held in fractionally by all the owners in the greater boundary. Ever see someone build a private swimming pool in the open space of a condo or other planned development?
The lawyer should access the subdivision planning docs and the legal map or record. In there he may find the anwser. My experience is adverse possession requires several triggers that may be impossible under the joint ownership of a hoa.
I would certainly ask for the "trespasser" to be levied legal fees.