Adjustawings hood, no ground?

Received the adjustawings medium defender. Thought about shortening the cable, so opened up the connection box on it to have a look inside - it would appear there is only live & neutral cables coming out of their lead, no ground, even though on the female connector at the other end of the lead there are 3 connections.
Is this standard?
I would have expected the ground wire to be fixed to the hood. I do have another lead also rated 10A (with what seems a slightly fatter cable).
Should I install this cable and ground the hood for maximum safety and minimum RFI?
 
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