Is it true that Harun al-Rashid killed Musa al-Kadhim?

Musa al-Kazim is Imam Abu al-Hasan Musa ibn Ja'far. He was nicknamed Al-Kazim for his suppression of anger (kazm al-ghaiz). Harun al-Rashid was displeased with him, and it is said that this was due to Al-Rashid's pride in his close kinship to the Prophet, peace and blessings be upon him, when he said: "Peace be upon you, O my cousin." Musa replied: "Peace be upon you, O my father," which angered Al-Rashid. Al-Khatib mentioned in "Tarikh Baghdad" that when Al-Rashid heard people pledging allegiance to him, he imprisoned him in Basra, then he was transferred between prisons until he died in the custody of Al-Sindi ibn Shahak in the year 183 AH and was buried in Baghdad. Al-Kazim died in prison and was not killed by Harun al-Rashid.