If parents treat that sort of behaviour as a game and chase her, cajole her etc. then she knows no boundaries. For sure she gets no leeway in the sense of pick an amount of space and if she moves more than 5 feet from you she gets a reprimand - so if you move she is responsible for moving too while at the park. At home keeping her at arms length or in the same area as you are in and letting her know why might help but not likely.
Play yard time in the house can work where she is confined to an area - can be sectioned off with shelves, furniture, gates, etc. till she earns the privilege of playing out might work. She has the self control of the infants/toddlers but the abilities of an older child but for all intents it is the same - she does not know how to play within limits so to start she has total limitations - here is your spot and here are your three choices of toys and remind her it is because she doesn't listen then expand her horizons. Much like we would do with a child that won't listen and pick up to stifle their mess making abilities for this child it is about redefining her ways of interacting with things.