This wikipedia tidbit backs up your point IN SPADES:
On June 1, 1964, Kenyatta became President when he successfully had Parliament amend the Constitution to make Kenya a republic with his office becoming executive President: the head of State, head of Government, and Commander-in-Chief of the armed forces.
Following the announcement in August that the Government would soon submit for approval a comprehensive set of amendments designed to transform Kenya into a Republic This Source Is Refering To August 1964: 3rd paragraph down - The Role Of The Senate In The Kenyan Political System - by J. H. Proctor, Jr.
Then there is this entry in Wikipedia on Jomo Kenyatta under Leadership (5th paragraph down.)
On June 1, 1964, Kenyatta became President when he successfully had Parliament amend the Constitution to make Kenya a republic with his office becoming executive President: the head of State, head of Government, and Commander-in-Chief of the armed forces.
I dont put a lot of faith in Wiki but it was this entry that had me looking elsewhere to confirm. I still have found nothing about the June 1, 1964 event.
NYT article from Aug. 15, 1964 Kenyan Leader Announces Plans for Republic
Wiki isn’t always something you can “take to the bank” but in this case it backs up a common sense interpretation.