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Well, it seems likely they were less-well adapted to local diseases than the locals. But I'd guess that childhood exposure may be enough to explain this, plus cultural adaptation? They certainly died in large numbers, in early days; IIRC, only 10% of Company employees made it alive to retirement back home. (I presume, but don't know, that more upper-class Mughals survived to equivalent age.)
Also, as TFA mentions in passing, many of these were the same strategies as practiced by upper-class locals: "adopted punkhas from the Mughals", swung by servants of course, wore light clothes, adopted a schedule designed around heat, not around far-northern winter daylight hours.
So, if you see someone driving a tuk-tuk, or rickshaw as they're known in Pakistan, you refer to the driver as a rickshaw-waala. A chai seller becomes a chai-waala, a fruit seller becomes a fruit-waala, and so on.
(Kipling also wrote SF short stories, set in a universe with the aforementioned organization as a world government, for example "As Easy As A.B.C." (1912).)
I remember hearing it for the first time watching reruns of It Ain't Half Hot Mum.
Also the British got their foot hold as Indian princes hired British and French mercenaries and had not read Machiavelli