No, it's untrue. Not that white men get paid more--that's true--but that it's an option. I can choose to improve my negotiation skills and my BATNA, so those are options. If you aren't already a white man, being a white man is not an option for you. We're talking about what our effective options are and that's just not one of them.

(Regardless of whether gender transitions count as a choosing to become a man, I don't think it would do much to boost income in our current society.)