I have to politely disagree, bridey. Dogs do form pack relationships with other animals, including people. I live in the heart of Texas sheep country, and livestock guarding dogs are extremely popular here. To train, a young 8-week-old puppy is put into a pen with a gentle female sheep (ewe). Human contact is very limited. The pup bonds with the sheep, and recognizes sheep as its pack. That's all there is to it: no formal training of any kind. I don't think such a relationship would be possible if dogs didn't "pack" with other animals.
Also, dogs are social animals who have an instinctive need for packs. You don't see a dog willingly on its own, and if it is, it's usually miserable. If you have only one dog, who else does your dog have to pack with except its humans? Since there are many happy, well-adjusted only dogs out there, they must be getting their pack needs met quite well by their families.
I have also had a dominant dog. I wouldn't call it being "pushy", "demanding" or any other name. He thought he was the leader, plain and simple. It took a lot of training and constant reinforcement to overcome it.