If not, how do they know that the deviation was in fact caused by twisting space time?
The GP-B experiment measured this effect and found agreement with the GR prediction. This does not prove that GR is correct; rather, it is a piece of evidence that implies GR is more likely to be a correct description of gravity than what we previously believed . Because the prediction was quantitative, it is unlikely that the result is caused by something else, which makes the evidence in favor of GR that much stronger.
Now, control groups are often used in life sciences fields. For example when you test a drug, you have a control group that takes placebo. It's not my field but as far as I understand this is done for two reasons. First, there is no quantitative prediction regarding how effective the drug should be, because drugs are not understood so precisely. So the prediction you're testing is much weaker; it's just a boolean. Second, there is a known effect -- the placebo effect -- that can affect results. In other words your null hypothesis is that there may be some effect. These things mean that, without a control group, the evidence in favor of a drug's effectiveness is not very strong.
 That is not to say that we believed GR was wrong, but we can never be 100% sure, and every piece of positive evidence strengthens the case.
If you accidentally did an experiment where GR and Newton predict the same thing, the control would kick in and tell you that you hadn't proved anything.
> Second, there is a known effect -- the placebo effect --
> that can affect results. In other words your null
> hypothesis is that there may be some effect. These
> things mean that, without a control group, the evidence
> in favor of a drug's effectiveness is not very strong.
In order to keep confounds in check, scientists attempt to keep everything either equivalent (by matching samples as precisely as scientifically feasible) or randomly distributed (by using, for instance, Latin squares and other randomization techniques).
They perform the experiment and obtain result B. This disproves Newton's theory immediately, and confirms Einstein's theory. We don't know that it is right, only that it has successfully made a prediction about something that hadn't been tested at the time the theory was developed.
Testing a place in space-time that should not be twisted would provide another element of confirmation, however the strongest and most interesting tests are those where the two theories differ in their prediction, not where they agree.
The experiment set out to experimentally test the accuracy of Einstein's predictions. The results of the experiment showed that under these specific circumstances, the predictions line up extremely well with observations.
There's no "control group" for this kind of test. Of course, they could potentially run multiple experiments to verify Einstein's predictions under different circumstances. That might provide useful information, but the lack of such information in no way discredits the results of this particular experiment.
If you want to read more about the experimental protocol, check out the final results paper: http://arxiv.org/pdf/1105.3456v1