You are partially correct... The 560Sl came with Limited Slip, not positraction. According to my research, all 560SL's came with limited slip diff. The limited slip relies on brass slip-ring mechanism which, over time, becomes less effective. This renders the rearend more akin to an open diff like earlier SL.

There is a fundamental difference whether the car is moving straight forward, or in a turn.

Your symptoms imply the limited slip is still functioning... If the diff were to lock up, steering would be compromised and the car would tend to understeer terribly (heading you for the ditch at a rapid pace). The fact that the unloaded tire is spinning does not mean the loaded tire is not pulling or applying force to the ground. The loaded (outside) tire has to turn faster to cover the ground relative to the inner tire (as the outer tire is traversing a longer path in the same time period). The inner tire is probably spinning because it is trying to match the outer tire's speed. If this is the case, the tire has only one option, and that is to break free and spin.

Perhaps someone here can add with the correct way to test (without performing numerous burn-outs)... I can't remember right now. I believe your diff is functioning normally, and is functioning as was designed.

Hope this helps.