I was clicking around that site again (www.mercedes-benz.com/e/default.htm), and by comparing the three engine options (500 and 320 gas, and 400 diesel) in two body sizes (Station/Long and Station/Short), it seems that the body size is one of two towing capacity factors:
All three engine options (even the small 320) are rated 7,700 lbs in the long wheel-base versions; and all three engine options (including the high torque 400-diesel and high powered 500) are rated only 6,283 lbs in the short wheelbase body.

I guess it's only a question of having enough mass (inertia) to properly control the trailer, rather than enough power to pull (which all the engines, even the little 320 gas) apparently have. Which doesn't say much for the M-class, which is rated (at least here in the USA) at only 5,000 lbs whether you have the 320 or the 430 gas engines.
But the second factor will surprise you even more (next message):