Lib/idlelib contains a startup file 'idle.py' (and 'idle.bat' and 'idle.pyw' on Windows).  IDLE, and I, have no control over the installation of IDLE, including the addition of system-specific auxiliary startup files and entries, with names containing 'idle', outside of /idlelib.  On Windows, there is no addition in pythondir/Scripts.  The 'IDLE' Start menu shortcut run idlelib/idle.pyw.

I believe IDLE's only manipulation of sys.path for the user process is to prepend '' or the the edited file's directory.  In my message above describing a possible experiment, 'sys.python' should be sys.path.  You can keep exploring if you want, but I am closing this for now.