Hello everyone

For a long, long time, I have felt uncomfortable as to whether Walter Ormiston MacKay was buried at Camp Bay Quarantine Cemetery. It's a case of conflicting information. First let me give you a little background:
Walter (born October 12th 1862 Kildonan, Sutherland, Scotland) He was the son of Robert and Elizabeth MacKay. Walter was also a brother to Jessie (NZ Poet), Walter Ormiston (named out of respect of Walter), Eleanor (Nell), John George, Isabella Esther (Tibby), Herbert (Scott), Agnes Emily (Ness) and Georgina (Tink). Walter and his parents came out to New Zealand in 1863 on board the SS Brothers' Pride which anchored at Camp Bay (in Diamond Harbour) on the morning of December 9th 1863. All passengers were placed in quarantine.
Findagrave link:
https://www.findagrave.com/memorial/259738084/walter-ormiston-mackayThe research thus far:
Walter died 9 months from croup according to the book "A Voice on the Wind" (written by Nellie F.H. Macleod, about the life of Jessie Mackay). I, myself, have yet to read a copy of this book.
A good portion of the passengers were released from quarantine on January 6th 1864. On that day, the doctor for the SS Brothers' Pride wrote a letter to the Health Commissioner (Doctor Donald) in which he describes of 2 deaths occurring in quarantine (Hathaway & Trigg). It also describes of a steamer (called Gazette) picking them up (except for a few - four - as there was not enough room on the steamer) taking them to Lyttelton & Chistchurch.
A later letter from Dr McLean, written on 16 January 1864, states that there are only three patients left at Camp Bay – all adults: a young man, and two women who had just given birth, and that he expected they would all be well enough to leave the following week.
In 1913 there was a reunion held for 50th anniversary of the journey of the Brothers' Pride - in a newspaper it describes of 4 deaths occurring in quarantine.
If you visit this link:
https://my.christchurchcitylibraries.com/blogs/post/jessie-mackay-poet-and-crusader/ it describes of quarantine at Lyttelton - I, myself, naturally thought this to be a mistake and to be referring to the quarantine barracks at Camp Bay. But this does back up the claim of 4 deaths occurring.
My questions:
Do you think it is possible, when referring to 4 deaths, 2 of the deaths might have occurred actually at Lyttelton, at its quarantine barracks there?
Thank you very much for your help,
Ashley