Having looked further at Elizabeth I can't see any evidence that she claimed to have been born in Bombay (in contrast to her sister Caroline).
1871 census: Shows Elizabeth (21 b East Indies) married to Thomas BUCHANAN (22 b Liverpool) in Toxteth Park with sister Caroline (22 b Bombay East Indies). RG10/3799/80/41.
1881 census: I cannot easily find them.
1891 census: BUCHANAN family in Toxteth Park; Elizabeth aged 36 and born "Point de Gall, India" - this is in modern Sri Lanka. RG12/2931/95/15.
1901 census: Elizabeth BUCHANAN (now widowed) in Toxteth Park aged 46 and born "India". RG13/3430/11/13.
When and where did the Thomas BUCHANAN/Elizabeth MURRAY marriage take place, and what details were given as to Elizabeth's father's name and occupation?