bman it is on case by case basis. Many of our HOA lakes have two thigns basically the lkae is in the neighborhood and owned byt the surrounding homes or it is in the bylaws it is common property and anyone that lives there can fish it.
Common property is good if wanting more money to help manage bad if wanting more exclusive rights. If owned by neighbors you can set rights and write up some bylaws to go by. And yes signs help keep out unwanted visitors. However if only one guy says I own it and I can let anyone i want to fish it he is propbably correct.