Let's say you're running an A/B test on a website. Let's also say the standard methodology of randomly displaying one version or the other is unusable due to SEO hand-waving. The particular page under test is localized to each city, so the best testing methodology your one stats-educated programmer could come up with is to randomly divide the population of cities into test and control groups.
Now it's a number of weeks later and you have results that seem valid, but that don't satisfy the business people driving the test. They want to switch the test and control groups and re-run the test. This doesn't seem right to your programmer, who would prefer to re-randomize the cities.
Would flipping the test and control groups have any validity at all? Is there any conceivable reason to do that instead of re-randomizing?
Edit to add: Each group contains just over 8000 cities (all in the US).