I have no problem with this. Everybody involved is consenting. The government shouldn't have a monopoly on space travel. So long as this project doesn't harm anybody without their informed consent, any government action to prevent it would be overstepping their bounds and infringing on personal liberties.
Between the government and big corporations, I trust them equally NOT to be ethical. But at least big corporations admit it.
I also think the government should be exploring space for the betterment of mankind, I just don't think anybody involved in government is genuinely interested in doing so.