He worked with cardiac surgeon Christiaan Barnard at the University of Cape Town, where he was involved with organ transplant research on animals and trained medical students in surgical techniques.

Following his death, controversy arose regarding false claims in multiple obituaries, including those published by at least five periodicals and the Associated Press, that stated he participated in the world's first human-to-human heart transplantation in 1967.

[5] Naki first performed anaesthesia on animals for Barnard, but was then "appointed principal surgical assistant of the laboratory because of his remarkable skill and dexterity.

"[7] Barnard was quoted as saying "If Hamilton had had the opportunity to study, he would probably have become a brilliant surgeon"[9] and that Naki was "one of the great researchers of all time in the field of heart transplants".

[7] After retirement, Naki helped the community of Kentani, where part of his family lived, for example "in the construction of a school and in the provision of a mobile clinic"[7] by soliciting donations from his "medical contacts".

"[6] After Naki's death, obituaries published 9 June 2005 to 2 July 2005 in at least two medical journals (The BMJ and The Lancet), one magazine (The Economist), two newspapers (The Independent and The New York Times), and an unknown number of newspapers publishing Associated Press stories, printed obituaries that made the following claims about Naki's participation in the world's first human-to-human heart transplantation: Between 14 July 2005 and 3 September 2005, the five aforementioned periodicals and the Associated Press issued formal retractions of statements in their obituaries of Naki that claimed that he participated in the world's first human-to-human heart transplantation.

Examples include: A 2007 book traced the origin of the incorrect story to a 1993 article in the Associated Press that stated "Barnard had Naki on his heart-transplant backup team.

… When Barnard performed the first heart transplant in 1967, Naki was part of the backup team at Groote Schuur Hospital in Cape Town.