Yes, Six Flags had the responsibility, both legally and ethically speaking, to take all possible measures to ensure the safety of the amusement park visitors. Engineers and other various inspectors are required to go over all the details of the park and the rides, so something like a tree too close to a roller coaster should not have been overlooked.
I believe there are always things that they could have done better in order to prevent an accident. It is not a shock that tree branches occasionally fall especially when dead or during a large storm. Six Flags should have been monitoring the trees better especially if they were that close to the tracks and had the ability to fall on somebody during a ride.
When a customer decides to get on one of the rollercoasters at Six Flags, they're trusting that absolutely everything is under control. For something like this to happen, not because of mechanical failure, but because of a tree branch, tells us that those in charge of safety had become complacent. They should have either seen and cleared the branch, or kept the trees trimmed away so that landing on the track couldn't happen in the first place.
By choosing to ride a roller coaster you are inherently putting yourself at risk for injury. Six Flags could not have done anything to prevent this accident. By going to 6 flags you accept that they do basic maintenance on their rides, but that there is always a chance of injury and that is a risk you must take.