You have to be resident within the district for three months - so if the issue would substantiate you would have to show that you moved within a certain district three months before applying at the e.g. Nebraska Service Center (and respective DOS).
You have to list a history of your current and prior addresses ... that is where this requirement would/could be verified. So if moved you'd be traveling after that for two or some weeks this would not matter as far as this issue is concerned.
My guess that this rule has been established to avoid 'Service Center Shopping' (and respective 'DOS Shopping') since some SSC/DOS seem to be able to process petitions faster than others - due to their workload, I assume.
Alex