What is the truth behind the story of Anas ibn Malik and Al-Hajjaj?

Al-Dhahabi mentioned that Anas ibn Malik, may Allah be pleased with him, was loyal to Abd al-Rahman ibn al-Ash'ath and incited people to fight al-Hajjaj. When al-Hajjaj's men captured him and brought him before al-Hajjaj, al-Hajjaj spoke in a vulgar manner unbecoming of the servant of the Messenger of Allah, peace and blessings of Allah be upon him. So Anas wrote to Abd al-Malik complaining about al-Hajjaj's disparagement of him in front of the "weavers of Basra." Abd al-Malik then wrote to al-Hajjaj, ordering him to apologize to Anas. When the letter reached al-Hajjaj, he went to Anas and apologized to him, saying: "My situation and yours is like the saying: 'I mean you, but listen, O neighbor!' I did not want anyone to have a claim against me."