arcpy.SetProgressor("step", "Processing...") do stuff... arcpy.SetProgressorPosition(3)
In a stand-alone script, your script isn't being called from an ArcGIS application, so there is no progress dialog box, result, or Python window where your messages can be viewed.
OK, well... I spoke too soon. I looked at the help that you linked and I still don't really get it. I still don't see how to tell it to display the step progressor each time it updates (steps).
Have you found any way to override or supress these other progressor messages from Esri?
No. But, this is a little bit moot as the progressors are not out front anymore (ArcMap background processing, Pro).
The help I linked is about printing messages -- which is what you have to do in scripts not run as a toolbox's script tool.
The help for SetProgressor has a code sample at the bottom on how to update progressor messages and the progressor "bar graphic".
I've found that sometimes progressor messages from tools you are running (especially spatial analyst tools) trump your progressor settings. In those cases the progressor doesn't always do exactly what you want.
SetProgressor only takes effect when you run the script as a script tool from within an ArcGIS application (ArcMap, ArcCatalog, etc.). Running it standalone or from a Python IDE/interpreter, it will not display the progress dialog.