If your thruhull fittings are original bronze, as mine are, they are insulated from the hull to prevent forming a battery from the bronze-water-aluminum mixture. Those fittings should not, as far as I know, be attached to the green ground. If they are, then current can flow between the bronze and the aluminum (because the green ground goes back to the hull) and the aluminum will be the loser.
If your thruhull fittings have been replaced with something like Marelon, then there are no worries.
The question I would ask the Triplite engineer is whether the ac output is isolated from the dc input, or whether the dc return (negative) is connected to the output green ground. I suspect that the latter is the case.
If the ac output is actually isolated, the connect the green ground to hull and the frame of your reefer, hook up the black and white, and you are all set.
If the ac output is tied to the dc input (connected from dc black to ac green) then your green is already tied to the hull. Just run green to the frame of your reefer, and hook up the black and white. If the frame of your reefer is already connected to hull through a reliable connection such as bolts or screws, then you do not need the green ground at all, it is already connected. Best marine practice calls for isolating the frame from the hull, and using the green ground.
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida