The twin paradox lends irrefutable evidence to the notion that time is nonlinear and controllable. In the twin paradox experiments have been conducted where one twin makes a round trip of a certain length and speed away from the Earth and back. Upon return arrival the twin who went into travel is a few years younger than the twin who did not travel. Therefore it is correct to say that time is not linear and controllable.
This question is one that many people have been asking for a very long time because the subject matter is not one that is easily answered. There is a large group of people that believe the answer is simple and a quick resolution can be had. But that is not the case in this situation. The twin paradox is quite challenging.
Even though the concept of the twin paradox is interesting, I do not think that its irrefutable evidence to the notion that time is controllable. I think that while the concept of time can be affected in some ways, it doesn't mean that events can be experienced again or changed.
Time is like another dimension, and you certainly cannot control the normal 3 dimensions of space anymore than you can control time. We can observe time but we have no way to interacting with it to change it, it is a train that can not be stopped, only theoretically slowed down and only at nearly impossible speeds to reach.
Any scientist who claims something is irrefutable is setting himself up for ridicule. There is simply too much we do not know or understand and theories have to be open to editing as new information emerges. Though the theory seems correct and is a good model, we lack too much information to call it irrefutable.