Is amputation applied if a person confesses to stealing something from a man, and the man confirms he has lost the item from his property?

Primary text

Amputation should be established when a person confesses to stealing an item from a man, and the man confirms, 'I have lost it from my property.' This is supported by the narration from Abd al-Rahman ibn Thaalaba al-Ansari, from his father, regarding 'Amr ibn Samurah ibn Habib ibn Abd Shams, who approached the Messenger of Allah (peace be upon him) and stated, 'O Messenger of Allah, I stole a camel belonging to Banu [clan name], so purify me.' The Prophet (peace be upon him) sent for them, and they stated, 'We have missed one of our camels.' The Prophet (peace be upon him) ordered that his hand be amputated. Thaalaba reported that he saw his hand fall while he was saying, 'Praise be to Allah who purified me from you; I intended for my body to enter the Fire.' This is recorded by Ibn Majah.