yeah, when i am out in the bush, in big bear or out in trabuco, i take my dog off leash and she acts 100% the same (she may walk a few more yards to the side but I can just tell her to walk at my heel if I want), but i still keep her on the leash just to comply with the law and make everyone else comfortable
even then, when i see dogs off leash at the park, I ask the owner if theyre ok with my dog playing before i let penny loose. I've never had anyone say no, but it seems it should be common courtesy before i let my dog run over to them.
i dont know if your dog has medical issues, or is being trained a certain way, so i just give a simple of "is your dog friendly? do you mind if they play?"
pic related, penny made a friend at the park that way