Can you explain the story where Sai Baba talks about being satisfied by food given to a dog? What was the deeper meaning he was trying to convey?

In a beautiful story from Chapter 9, a lady was confused when Baba told her she had satisfied his hunger, as she was dependent on others for her own food. Baba clarified the profound meaning behind his words. He explained that when she gave bread to a hungry dog that appeared at her door, she had actually fed him. He revealed his divine nature by saying, "that dog which you saw suddenly, I have oneness with him." He further extended this by mentioning his oneness with a pig as well. The deeper meaning, as Baba explained, is that he resides in all beings, and serving any hungry creature is a direct service to him. This lesson moved the lady to tears, realizing the vastness of Baba's presence.