I don't have an HOA but my property operates under deed restrictions that limit property owners in meaningful ways, establishing usage of the wells, easements, number of structures and so forth.
One of my neighbors repeatedly referred to herself as "the head of the HOA" and I told her she needed to stop saying that because we don't have one. I didn't say as much but I would hire an attorney to send a C&D if she were to keep that up.