Do animals heal their owners energetically via their intention, or does this simply allow divine intervention that can be enacted because the animals are in divine alignment?

Both things happen. Animals are better at self-healing and healing living things around them energetically through their own intention and energies than humans, who are in a highly weakened state with regard to their non-local consciousness. But their healing intentions will also call on the divine and their own efforts will be augmented many times by the divine to aid them and amplify their efforts to increase the effectiveness, the speed and depth of healing, and so on. There are many times companion animals want to heal their owners and run into trouble because they are unable to do it on their own and the divine intervention they summon is taking too long, and they might suffer personally through internalizing the conflict to work on it and drag themselves down, even to the point they might develop a fatal malady of some kind and perish, but are willing to do so because they are so devoted. Their purity of intention makes them very effective at eliciting divine support, much more so than with human beings who very much have a mixed history and a mixed agenda within, largely out of their conscious awareness, with many negative beliefs at multiple levels of the mind that work against them in receiving divine assistance effectively. The animals are quite effective at this because of their purity of intention and their selflessness. That is why they are truly divine messengers and helpers for humanity and so very effective many times in helping those around them.