But that has nothing to do with how M/S works. Lemme try to explain it simpler:
If you've read the big thread, you know that a cardioid pattern is made up of equal parts of an omni pattern and a figure 8 pattern. When the two patterns are combined 50/50, you get cardioid. The positive front side of the figure 8 mic combines with the all-positive omni and increases the output from the positive direction of the signal, the front. At the same time, the negative back side of the figure 8 exactly cancels the omni positive wave and you get the familiar cardioid pattern.
Now if you turn the figure 8 mic sideways and add an omni (or anything else) facing forward, AND invert the polarity of the figure 8 mic to another channel, here's what happens:
The positive signal from the omni and the original positive signal of the figure 8 combine to give you all the left side information. At the same time, the positive signal from the omni and the inverted (now positive, but inverted) signal of the figure 8 combine to give you all the right side information.
The cool thing is that it's still a combination of omni and figure 8 on the left, so you still get the usual cardioid pattern if you shut off the right side inverted "S" signal. It makes a cardioid pattern, pointing left. Shut off the left figure 8 pattern and bring up the inverted figure 8, combined with the omni, and the mic is now a cardioid, pointed to the right.
The level of the two figure 8 signals gives you the stereo spread, while the center mic gives you the mono information. If you collapse the stereo image by lowering the "S" levels (or centering the pan pots, the "S" information cancels out or disappears and you're left with a perfect mono signal.
If you think of M/S as Mono/Stereo rather than Mid/Side, it might make things easier to understand: The M mic track (from the forward facing microphone) contains the Mono information, and the two S mic tracks (from the sideways facing figure 8 microphone) contain the Stereo information.
Using a cardioid for the Mid mic results in the two side patterns acting like X/Y cardioids BUT, they collapse prefectly to mono.
The phenomena you're describing is caused by inaccuracies in the signals due to room reflections and differences in the signal due to other factors - it doesn't contain any stereo information. The "S" signal in M/S does - it contains all the stereo information, once properly decoded.