LW...it sounds redundant to me.
The battery is grounded to the Chassis of the car and if you connect (g) and (-) to the chassis of the car you are essentially grounding these wires. I see no need to run a wire to the battery for ground. And no you wouldn't need to fuse the ground wire from the battery to the PSU (if you decided to wire it this way...which as I said before doesn't make much sense.)
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