This is a very important point. Not just that, but the "offload person" won't be a member of the teamster's union (seeing as how they aren't actually driving the truck) and will have a more reasonable wage.
As chollida1 points out, UPS/Fedex may not be allowed to lift the CLD requirement quite yet, but that will probably come in time.
IIRC, If you are under 26,001 Lbs GVW you don't legally need a CDL (unless Hazmat). Some carriers like UPS/FedEX may require a CDL anyway, but that is a company policy.