"The inference is that being a white man is being honest and virtuous. Whilst being non-white has connotations of being disingenious or underhand."
Utter f*cking drivel, it has f*ck all to do with race and never has .
"Play the white man" goes back to the film industries standard of the goodies always had the white hat and outfit while the baddie was in black with a black hat, they were always the honest & virtuous one, just as calling someone a "Black hat" meant they were a "Baddie", after the sat morning showings kids were running around being either "The black man", or the "White man" from the 1930s.
Go back as far as medieval times and white was purity while black was evil, so all the cinema did was mirror it, no racial slant other than in the minds of people looking to take f*cking umbridge.