Saving as an application versus script

Here is my script:

    tell application "System Events"
       click menu item "Clear Menu" of ¬
           menu "Recent Items" of ¬
           menu item "Recent Items" of ¬
           menu "Apple" of ¬
           menu bar item "Apple" of ¬
           menu bar 1 of ¬
           (first process whose frontmost is true)
   end tell

Here is my challenge:

If I save this as a “Script” and then run this script within Script Editor, the script works.

If I first save this script as a “run-only” application, and then double-click on the resulting application, it does not work.

HAALP!!!

See my contribution towards the end of this thread.