Answer
While non-script core tools will work correctly, all script tools including the Spatial Statistics tools, Multi-ring Buffer, and any user created custom tool will fail. This failure is not a result of errors in the script(s) but rather a problem with the data locking mechanism in ArcMap that is designed to prevent concurrent use of a dataset.
The workaround is to save your map, close down the current ArcMap session completely and then re-open your map. Once ArcMap is re-opened, all script tools will work correctly with the newly created feature class.