Animal law: if one provides shelter, food, & water one is responsible for that animal - true or false?

Dog from another neighborhood constantly getting loose & coming to my neighborhood. Dog is taken in by neighbor receives food, water, & shelter but no means of containment. Dog is not dangerous. Dog runs to whatever human is out & about. Problem occurs when I try walking my own dog (on a leash). Dog interferes by putting itself between me & my dog which makes for very unpleasant untangling. Landed on my backside yesterday when my dog (on leash) tried to dominate interfering dog. Is the caretaker neighbor responsible for interfering dog? Neighbor claims cannot legally tie dog because not owner.