Just because the 2008 Olympics were successful, this does not mean is a fake.
What people don't understand is s explanation of his time machine is incredibly accurate. In other words we live in infinite parallel worlds with infinite outcomes.
Also, people also don't believe that time travellers can lie and spread disinformation for their purposes.
The fact that the olympics in 2008 were successful, just may mean was successful in his mission, and we won't have the terrible outcomes like WWW3.
Right now WWW3 is still possible, just look at the situation with Russia and America right now.
Let's just pray the timeline has diverged enough and we are not on the similar timeline as was on. That really is a truly awful future.