staring in your face, waiting to be noticed:
there is a "Prime Minister" in UK, not in US.
And in UK there are plenty of bodies headed by a "Chairman" nominated by the Prime Minister (see QUANGO
https://en.wikipedia.org/wiki/Quango and also
https://en.wikipedia.org/wiki/Talk:Quango etc.).
IOW here a "political nominee" is someone who ended up being a "Chairman" of some government controlled "external body" simply because "politicians/people exercising public authority" put him there. Any real competence being surplus to requirement and only ever present by pure accident... a bit like ministers.
one example: the Chairman of the BBC (British Broadcasting Corporation
https://en.wikipedia.org/wiki/BBC ) is a "political nominee" designated by the Prime Minister.