Why did Prophet Muhammad stand up during a funeral procession of a non-Muslim?

Salaam.Please refer to the two hadiths below.Narrated Jabir bin ‘Abdullah : A funeral procession passed in front of us and the Prophet stood up and we too stood up. We said, ‘O Allah’s Apostle! This is the funeral procession of a Jew.” He said, “Whenever you see a funeral procession, you should stand up.” Bukhari 2:23:398………………………………………….. ………………………………………….. ….Narrated ‘Abdur Rahman bin Abi Laila: Sahl bin Hunaif and Qais bin Sad were sitting in the city of Al-Qadisiya. A funeral procession passed in front of them and they stood up. They were told that funeral procession was of one of the inhabitants of the land i.e. of a non-believer, under the protection of Muslims. They said, “A funeral procession passed in front of the Prophet and he stood up. When he was told that it was the coffin of a Jew, he said, “Is it not a living being (soul)?” Bukhari 2:23:399The above two hadiths have been explained by a brother in this manner: “we learn the underlying cause (Asbaab-ul-Hadeeth اسباب الحديث) through authentic sources that Allaah’s Messenger Muhammad صلی الله عليه وسلم stood up so that the bier would not pass above the heads of the Muslims, as this is a form of humiliation to them. If this is the underlying reason (which in fact is) for his standing up, then the practice of standing up for a bier (Janaaza جنازه) will be restricted to the bier of a disbeliever.But i and all my other muslim brothers and sisters have always known that the Prophet (s) stood up because of what he said in the hadiths and basically to show respect to humanity.What is the correct explanation?jazakzwsalaam