I think you are misunderstanding the idea of a scientific theory being "true" until it's disproven.
The scientific method progresses by people proposing theories about the universe and how it works. For a theory to be scientific, it must be falsifiable. This means that you can do an experiment that disproves the theory. For example I could have some ideas about gravity that results in a conclusion that apples will fall upwards if I drop them. By doing an experiment, I can show that apples do not fall upward when dropped, and therefore the theory must be false because its predictions are wrong.
When you are referring to a theory being "true" in your question, I suspect what you really mean is that the theory is falsifiable because it makes predictions that can be tested with an experiment, but that no one has done the experiment to falsify it yet.
There is another sense of a theory being "true" in science, and that is one in which many, many experiments have been performed, and none have managed to falsify the theory yet. Instead, the theory makes predictions and the experiments continuously confirm the predictions. However, there may still eventually be an experiment performed that disproves the theory. For example, the Newtonian view of physics is a view that was true in this sense despite much experimentation for hundreds of years. But nowadays it can be shown to be wrong via experimentation.
Regarding your question, I suspect that the problem atheists have with theists is that the theist's claims cannot be falsified in a scientific sense. There is no theory of the form "if God exists then predict A,B,C..." So the atheist cannot perform any experiment to disprove the theory. When you say they put the burden onto the theists, maybe they are in fact asking for a better scientific theory about God -- which may not be possible given that science deals with the material world and religion the spiritual.