Why did Ibn Zubayr Detain Ibn al-Hanafiya?

[Cherub786]

I greatly respect sayyidina Abd Allah b. Zubayr رضى الله عنهما not just because he happened to be a Sahabi, but because of his courage in launching the armed uprising against Yazid and the Umayyad regime.
However, I am disappointed to learn that Ibn Zubayr mistreated some of the Ahl al-Bayt, specifically, sayyidina Muhammad b. al-Hanafiya رضى الله عنه. From what I have read in the Tarikh of Imam al-Tabari, Ibn Zubayr had Ibn al-Hanafiya and some of his relatives imprisoned at the well of Zamzam, because of their refusal to make bay’a to him. Ibn Zubayr gave an ultimatum to Ibn al-Hanafiya to swear bay’a to him otherwise he will have him burned alive. The situation was so dire that Mukhtar al-Thaqafi had to send hundreds of his troops to Mecca to rescue Ibn al-Hanafiya.
How genuine is this story, and is it a well known historical incident or a tale told by Abu Mikhnaf?

[Cherub786]

Apart from Tabari, Ibn Athir has also recorded this incident in al-Kamil fil-Tarikh. He has mentioned all the same details, i.e., Ibn Zubayr imprisoned Ibn al-Hanafiya in Zamzam along with his relatives and dozens of others because they refused to give him the bay'a. He threatened to have them burnt alive, but two days before the ultimatum, Mukhtar's troops arrived, wielding sticks (thus became known as the Khashabiya) and rescued Ibn al-Hanafiya.

Ibn Athir explains that Ibn Zubayr was afraid that Imam Ibn al-Hanafiya would declare his own caliphate, as Mukhtar and his party were calling for him, and this is the reason why he had him imprisoned and pressured him to give him the bay'a:

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