I have a ton of SKB cases, but the recently discontinued ones with the aluminum valance, I'm sure the new ones are still good (though the handles look way less heavy duty and I'm not sure they still have replaceable nut clips if you manage to strip the holes).
Anyway, the way they measure them can be confusing, basically the shallow ones are 10.5 inches from front rail to back rail, but they also give you the measurement to the back of the rear lid (and I think from front lid to back lid), basically they're saying there's room in front for the rack handles, knobs, etc. and a bit of room in the back for wires if you're up to the rear rail with the unit you have mounted in the rack...
I'm not sure I've seen the exact dimensions of the III, but I know Cliff said it's around 10 inches deep so the shallow rack could work, but would be fairly tight in the back, personally, I'd go for the standard depth rack, more room is generally a good thing!
Hope that helps!