Thanks for the additional information. I asked where the dog was petted because the breed does tend to have some issues with the discs in the back. Sometimes these dogs will not want anyone petting them for fear they may touch a spot that might cause them discomfort. The only way to rule that out would be to have special imaging done. Actually any pain might cause a dog to be aggressive. There is also other conditions such as hypothyroidism that can cause aggression as well. You can read about these on the sites below.
If there is no medical cause for the aggression, then it is strictly behavioral. Dogs are aggressive toward people for a variety of reasons. It might be that they are fearful of people and thus are aggressive before the person can be. In other cases, a dog is aggressive in order to dominate the people. Other causes could be that the dog feels they are the alpha member of the pack and as the alpha member they must protect the pack (you) from threats (people). In this case, it is hard to tell what the cause is. Your parents haven't had her for that long, so I doubt she feels protective of them and your mom wasn't there. I suspect it may be partially dominance or fear based. When people lean over them, it may be seen as a dominant gesture and thus they lash out since they are dominant or fearful.
In addition, owners sometimes make the situation even worse by tensing up and worrying about what will happen. The dog senses the owner worry and feels that she is justified in her aggressive stance because the owner is worried about the people. They don't know they are worried about them attacking, they just feel that the ownerr is worried and assume it is the people. Not sure if this has been an issue yet but it may become one as your parents become more worried about the situation.
Whether dominance or fear based, many things work for both. Obedience training really helps. It establishes the owners as the boss and the dog as the submissive member. As the boss, it is the owners job to protect the dog. So your parents would have to not let people pet the dog until the dog is more comfortable around other people. Obedience training also helps teach a dog what humans expect and thus the dog gains self confidence and is less fearful. So obedience training is a must. The following site is helpful for teaching you how to train your dog. Be sure and click on the link to the page on obedience at the bottom. and links on subsequent pages leading to detailed instructions.
Training works best if you train at least 30 minutes a day (two 15 minute sessions). I would suggest that your parents start making the dog work via the Nothing in life is free program (NILF). It is outlined below.
Putting a basket muzzle on her may help prevent bites when away from home and when visitors are present. It will definitely make your parent feel less anxious.
I would have them also try to do group classes so the dog is more socialized in a controlled atmosphere.
It will be helpful if theycan find someone to help them once they have the dog listening to commands consistently. The dog will be on a leash. They will have the helper off in the distance. THe helper will gradually move closer to them preferably walking past their position in the distance. As long as the dog ignores the helper, they can give the dog praise and a treat. The second they see her fixate on the person or show any other sign of aggression (hair standing up, etc.) give the dog a correction by giving a short tug and a firm low toned "NO". It shouldn't take the dog long to realize they will not tolerate the aggression and that if she ignores the person, she gets treats. Once this happens they can repeat the training moving the person closer until she is no longer trying to bite people. Now if she only does it when they lean over her, then have them do that. The idea is to try and trigger the behavior and then reprimand her for the undesired response and reward her for the desired response.
In addition, if the situation is not improving using the techniques I describe, they may have to consult a professional behaviorist. You can usually find a behaviorist by asking your Vet for a recommendation or you may be able to find one using the following site.
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Since there have been recalls on certain foods, please check the following site to be sure the food your animals eat is not affected. If it is affected, contact your vet as soon as possible. Have your dog seen if they have any symptoms.