He tried to intercede

By this point Usamah was someone people went to when they wanted the Prophet's ﷺ ear moved. He had grown up in that household; asking him to speak up for you was a reasonable thing to try.

A woman from a leading family in Makkah had been caught stealing. Word went round that the matter would go badly for her, and some of her people wanted her spared the punishment. They came to Usamah and asked him to intercede.

He raised it with the Prophet ﷺ.

The Prophet's ﷺ face changed as he answered. He asked Usamah, in substance, whether he was interceding regarding one of the punishments God had set.

Then he stood before the people and spoke plainly: those who came before them had been destroyed for exactly this — when someone with standing among them stole, they let it go, and when someone without standing stole, they carried out the punishment. And he said that if his own daughter Fatimah had done what this woman had done, he would have had her hand cut off the same as anyone else.

The punishment was carried out.

The report does not read as a story about Usamah being disgraced. He asked; he was told plainly why the request could not be granted; the principle mattered more than the relationship. What it establishes is that closeness to the Prophet ﷺ was not a channel for bending the law, not even for the person he was closest to.

The account is in both Sahih collections.