Time Travel... What would happen?

There's a new movie in the works based on one of my favorite short stories. The story is Ray Bradbury's 'A Sound of Thunder' from the book 'R is for Rocket' It involves a future where time travel is not only possible, but is a business.
Hunters are taken back in time to be given the chance to kill a T-Rex. As preparation for the trip, advance squads are sent out to determine the exact time of the Rex's death, where he'd fall, and lay down a path for the hunters. The hunters are told to do nothing but shoot the Rex. If they affect anything else or even step off of the path it could affect the timeline and the future would be altered. Even the bulletts must be recovered, to maintain the balance.
One person does accidently step off the path and during the return trip finds a butterfly stuck in the mud on his shoes. That one butterfly ends up changing the course of history over the millions of years, until when they return America is a total dictatorship and life is completely different than they knew.
I think that no matter what, even the existence of a human millions of year ago though would change the course fo history. At least the diseases that we have developed since then would cause catastrophe. There would be no immunity, so millions of animals could die.
However, other theories state the timeline would be unbreakable and that everything we do is predestined and cannot be avoided.
What do you think might happen?
Hunters are taken back in time to be given the chance to kill a T-Rex. As preparation for the trip, advance squads are sent out to determine the exact time of the Rex's death, where he'd fall, and lay down a path for the hunters. The hunters are told to do nothing but shoot the Rex. If they affect anything else or even step off of the path it could affect the timeline and the future would be altered. Even the bulletts must be recovered, to maintain the balance.
One person does accidently step off the path and during the return trip finds a butterfly stuck in the mud on his shoes. That one butterfly ends up changing the course of history over the millions of years, until when they return America is a total dictatorship and life is completely different than they knew.
I think that no matter what, even the existence of a human millions of year ago though would change the course fo history. At least the diseases that we have developed since then would cause catastrophe. There would be no immunity, so millions of animals could die.
However, other theories state the timeline would be unbreakable and that everything we do is predestined and cannot be avoided.
What do you think might happen?