What is the difference between "double dissociation" and simply having control and experimental groups? According to my textbook Cognitive Psychology by E. Bruce Goldstein,


  a double dissociation occurs if damage to one area of the brain causes a function A to be absent while function B is present, and damage to another area causes function B to be absent while function A is present. To demonstrate a double dissociation, it is necessary to find two people with brain damage that satisfy the above conditions.


I don't understand how this is any different from merely having a control group and experimental group. Suppose I take a group of people who destroyed hippocampuses and observe they cannot store episodic memories. I then take a group of people who have hippocampus and observe they can store episodic memories. This tells me the function of the hippocampus must be in part to store episodic memories.

My Question:

How does a double dissociation yield information any different from this?
In brain damage/lesion studies, a double dissociation gives evidence that function A and B are, to some degree, implemented in different regions of the brain. In general, a double dissociation shows evidence that A and B are independent of each other.

This is a different kind of claim than saying that function A is implemented in brain region X. For this kind of claim, performing an experiment that lesioned (removed) a brain region in some subjects but not others (obviously not an ethical experiment, but let's ignore that) would be a reasonable way to test the claim. 

However, this kind of experiment wouldn't be able to provide evidence that functions A and B are implemented in independent regions. To illustrate why, let's consider the possible outcomes of the experiment:


Functions A and B both remain in tact or Functions A and B are both disrupted. Clearly this outcome doesn't provide any evidence that A and B are implemented in different regions, since both functions are affected equally by the lesion.
Only function A is disrupted, function B remains in tact. The most that this outcome shows is that region X (the lesioned area) is crucial for function A but not B. However, what is doesn't show is that function A is independent of function B. It could be the case that function A can be disrupted without disrupting function B, but that any disruption of function B will disrupt function A.