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I went back and reread from the beginning, instead of merely answering the question you asked when adding me as nosy. More comments:
Windows file associations are so disfunctional that you should not depend on them being anything in particular. I nearly always open files from within applications (IDLE for python files) or with RightClick context menu when an entry specifies the app that will be used (as with 'Edit with Notepad++' (getting Python make such is another issue). The only way I can run from Command Prompt is to cd to the appropriate pythonxy directory and enter 'python full\path\to\file' (with stupid backslashes or 'python -m module' (which looks for module under /Lib). 
In XP, and I presume later, the term 'DOS box' is obsolete and I would delete it. The 'Command Prompt' app (with caps) is found in the Start/Accessories directory. So I would say "open a Command Prompt window (in Start/Accessories)"
Back to your message where you added me. I am not sure of the difference between 'local script' and 'global command'. I do not understand your proposed note, especially "*include link to relevant section of docs.python.org/using*.".
Script run without extensions when run with an explicit python command.
I was primed to answer this because someone recently, on the tracker or python-list, proposed to 'fix' a problem (wrongly) by adding a .py(o/w) extension check to determine if a file is Python code before running it.
I am not sure what 'or does the installer add .py?' could mean. The Windows installer? 'Add' to what? 
I realize that my answers may appear naive. I hope usefully so. I have used Windows since Win95 and have learned to focus, as described above, on what dependably works with minimal surprise. The extremely few 3rd party Python-based stuff I have installed has either come as a zipped library I could extract into site-packeges or as an independent app to be unzipped elsewhere or installed with a Windows-style installer. I have never used setup.py so no expert advice on its successor from me.