Certainly… not to say there is no instinctual sense… it’s just that I don’t think it’s the important aspect. That sense tends to be with respect to some current activity that might be disrupted… like a enjoying the bone.
It’s as much as “don’t mess with what I’m doing” as much as it is “I own this”.
Since we’re on the subject, one unique expression that seems a lot closer to human ideas of ownership is that of being territorial. I’m guessing that to the instinctively territorial animal it feels more like a trigger for aggression toward a competitor. An owner asserts full control. The territorial animal just doesn’t want you around.
Back to your regularly scheduled program.