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The stability control uses the brakes to try and prevent a skid, it does not work, all you get is beeping and flashing warning lighs on the dash. You’re skidding because you lost traction, using the brakes to try and gain traction does not work. You’re not missing anything.
If the stability control works like it did/does in our MLs, it works by applying light braking to only the wheels that have lost traction and are spinning, thereby transfering power to the wheels that have grip. It's a very smart system and in this case, through computer controlled application of independent braking to each of the four wheels individually, braking does indeed work. Human braking of all four wheels will not restore traction, of course, but that's very different. ABS helps retain some steerability if you mash on the brakes, but I still lightly pump... old habit, but still a good one. Can't bring myself to trust ABS over good driving technique.