In the results area of the Near Me widget, default text is displayed which reads 'Closest Address' and then displays the location from which the search was initiated - not the closest address. The phrase 'closest address' is misleading, well actually its just wrong - it is not the closest / nearest address. The confusion created by that phrase has lead my client to remove the tool from their app.
In the simplest case, the 'Closest Address' text is hidden or re-written to correctly say something about the location being the center of the search radius. In the best case, the text is configurable.