[raganwald]

They don't actually know that the deviation was caused by the twisting of space-time (and neither do we). What they knew before conducting the experiment was that they had a theory (Newton's) which predicted result A, and another theory (Einstein's) which predicted result B.

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.