The placebo effect. Belief in a substance is only one mechanism of placebo action. Suggestibility and conditioning are among some others. Animals are subject to both. Recall Pavlov's classical experiments.
Animals also respond well to attention by humans.
Further, whether the animal is better or not is determined by humans observing the creature, not objective reporting by the animals. Natural ups and downs of symptoms or natural remission. Such responses can be long term and are unpredictable. The remedy contains an effective dose of real medicine. There is no way of interpreting the labels of homeopathic products because active ingredients are not quantified.