Scripting BTT's own keyboard shortcuts without invoking action "Send Keyboard Shortcut"

When I assign a keyboard shortcut to a BTT action, such as "Toggle Do Not Disturb On/Off", I can use BTT's built-in "Send Keyboard Shortcut" to trigger this action with the BTT assigned shortcut. However, I cannot trigger this same action using a fairly standard keystroke script within BTT's "Run Apple Script", such as:

tell application "System Events"
keystroke "D" using { shift down , control down , option down , command down }
end tell

I ended up assigning this very keyboard shortcut in System Preferences->Keyboard->Shortcuts->Mission Control->Turn Do Not Disturb On/Off, and the aforementioned keystroke script will now work with BTT's "Run Apple Script".

These two ways of assigning keyboard shortcuts (in System Preferences and in BetterTouchTool) sound identical to me. What am I missing here?