As I understand it, Min Samples are the number of first ray hits on a pixel, if the results vary by the threshold level, then more samples are then throw at the pixel until it reaches it's maximum or a threshold level is reached.
So in the settings you used Frank, AA 24 with '1/16th first samples' you will have a minimum of 36 samples finding out what colour that pixel is. With dense geometry having only 4 initial samples, the threshold could be reached without having an accurate representation of that pixel. We've forced the issue in your render, by making sure we have 36 minimum samples to take an average from. With a threshold of 0.15, we are effectively saying, don't go onto the next level of sampling unless there is something really challenging to work out (your 36 results would have to vary by 0.15 between each other to trigger more rays).
In the default settings this threshold has a much lower decimal value, which allows more rays to be sent if that tight threshold level is not achieved.
How this all translates to mixing between adjacent pixels I'm not sure. And could be the reason for the 'blockiness' in your image (and mine looking back).
What is important about this technique is that you get an accurate main colour for your pixel, so that when the camera moves, the same area being sampled now in the next pixel, will give a similar result. Hence less noise between frames.