First point would be a reality check.
Even if, someday, the ability to travel in time is perfected or even achieved we will never be able to travel back in the past beyond the date of the discovery of the ability to do so.
If we would have been able to do that, we would already know that time travel is actually, and not just theoretically, possible.
Governments are almost always involved in research, Mr. Hatten - where are you, and any government funding that results in the achievement of time travel will make sure that only that government knows about the ability.
Thus, the question is moot as we may never know about the ability to, or not to, travel in time.