Either do it for every player, or use Shift+Click or Ctrl+Click to clear it for all players. I believe this can be answered in even the StarEdit help file.
EDIT:
QUOTE(StarEdit help file)
To set the initial Fog of War settings for each player, you can use the masking tools in the Fog of War Layer. These tools allow you to set areas of the Fog of War to be either fully or partially obscured. From the Layer menu, select Fog of War. Click or click and drag in the main window to mark areas as partially obscured. Painting over these areas again will change them back from partially obscure to fully obscure. The preceding method will uncover the Fog of War layer for the current player selected. To alter the Fog of War layer for all players in a scenario, hold down the [SHIFT] key while clicking in the main window.
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Ha.