This problem can manifest even with dogs that have been well socialized throughout their life. Your dog is obedient and cooperative with you so it's not necessarily practicing ranking with the owner. However, 90% of the time dogs practice ranking with one another is through possessing different objects, even if the object has a low reward value - just so they can show the other dogs who will be the top dog.

If your dog has formed too much of an exclusive bond with you it will see other dogs and people as a threat to the attachment between the two of you, and will guard you. It seems like the dog has got it in its mind that any toy or bone you give her is hers and she takes the liberty to aggressively protect it from any other being. This is inappropriate pack behavior and needs to be corrected before it becomes aggression. The correction needs to be delivered the moment your dog begins to stare at someone waiting for eye contact. The level of the correction also needs to match the level of intensity and drive of your dog.

As a dog trainer I've worked with this problem numerous times. I recommend keeping your dog on a leash while she is around other people and animals. Watch her very carefully. If you notice stiffness in the body or staring deliver a correction. Don't be harsh or angry with the dog but just grab her attention. She'll be happy to cooperate with you as long as she understand what you want from her.