A possible solution: Add a "Show Responses" button to the Chart Tool
I think the easiest way to integrate this would be to add a "Show Responses" to the bottom of the statistic page, and instead of running the summary reports, the user would go to the "Display Results Page", with an indication what what filter was set.

Right now, the only filter that "Display Responses" supports is "Complete/Incomplete/All", this would allow searching by criteria specific to the survey, e.g. a report of everyone who answered "yes" to the question "Would you like one of our salespeople to contact you?"

Alternatively, the filtering UI used for statistics could be added to the top of the Display Responses page.