If a scenario like this would generate major concerns for your reporting, a first advice might be simply not to allow tickets to be reopened. And yes, that might imply giving the closure of your tickets' process some thought (e.g. about a pre-closure step in the process, about some form of approval by the customer, ...). But once closed, you will be assured that the scenario described above will no longer be possible.
An alternative might be to not only report on your closed issues, but also on reopened ones. If you include reopened issues in your reporting, you will be able to account for certain deviations.
On a side note - you did not mention what kind of reporting you are actually referring to. Between the lines, I assume this is mainly regarding the built-in reporting that comes out-of-the-box with JIRA Service Desk (just guessing, I admit). You're kinda right about the shift that will occur there. But reporting there is mainly intended to show you from day 1 of using the product where you can improve. If you might need hardcore historical data for formal SLA Reports with consolidated periodical data, look into a solid BI-reporting tool like e.g. EazyBI. It will use your actual Service Desk data, but add the historical dimension to your reporting.
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