This experiment did not set out to "prove" anything. I think you'll find that the original article does not use the word "prove" even once.
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.
Comments
This experiment did not set out to "prove" anything. I think you'll find that the original article does not use the word "prove" even once.
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