That was with respect to his own personal rights. As for the limits set by Allah, the two Ṣaḥīḥ collections record from ʿĀʾishah—may Allah be pleased with her—that:

“Quraysh were deeply troubled about the case of a woman from the Makhzūm clan who had stolen. They asked among themselves, ‘Who will speak to the Messenger of Allah—peace and blessings be upon him—about her?’ They said, ‘No one would dare except Usāmah ibn Zayd, the beloved of the Messenger of Allah—peace and blessings be upon him.’ So Usāmah spoke to him, and the Prophet said, ‘Usāmah, are you seeking to intercede concerning a ḥadd of Allah’s ḥudūd (one of the prescribed penalties)? What destroyed the peoples before you was that when a noble person among them stole they let him go, but when a weak person stole they carried out the punishment. By Him in whose hand is my soul, were Fāṭimah the daughter of Muḥammad to steal, I would cut off her hand.’”

Allah has also described the community of Muhammad—peace and blessings be upon him—as the most beneficial nation for all people, saying:

“You are the best nation ever raised for humankind: you enjoin what is right, forbid what is wrong, and believe in Allah. If the People of the Book had believed, it would have been better for them; some of them are believers, but most of them are defiantly disobedient.” (Āl ʿImrān 110).