Science cannot prove that a theory is true. Is this true?

I would like to discuss the notion, developed by Karl Popper, that science can only disprove a theory. I remember reading somewhere that if a theory is proven wrong, then the complementary theory is actually being proven right, which would then contradict the claim that no theory whatsoever can be proven right.

Let's take an example, the climate, not only because the conference on climate change in Copenhague in on this week, but also because it is the system that I am the most familiar with. Say, a theory states that El-Niño is caused by wind bursts in the western Pacific. As long as observations show that wind bursts do occur before the start of El-Niño, you are only observing the facts that the timing of the events might be related but you are not proving that the wind bursts do cause El-Niño. Each can independently be caused by something else. However, if one year, there is no wind burst but an El-Niño, then you are proving that El-Niño is not caused, at least not all the time, by wind bursts. In this case, we have proven that the theory "wind bursts do not always cause El-Niño" is true.

The difference between the two theories is that the first one is a predicting theory which is supposed to work all the time, while the second is not; in other words, the first one is useful, not the second. To prove a predicting theory, you need to prove that the causation works all the time but because the world is infinite and open to the future, you can never prove it absolutely. The more the theory succeeds the tests, the more likely it is, but that is it, no certainty. However, to prove a non-predicting theory, only one example suffices, which we have done above. And so here is the crux of the argument: Formal definitions of theory do include that a theory should be able to perform predictions. So the second "theory" above is actually not a theory. And so yes, indeed, science cannot prove that a theory is true but it can prove other things!