Speedracer has a good point about looking at the aircraft as a system where all the parts work together and have an impact on one another. One aspect of the size issue is how tolerances impact the performance of the aircraft. Through the years I have had several 1/12 scale warbirds. These were generally small airplanes with a wingspan of three to three and a half feet. When everything was set up just right they were as stable as the big warbirds. Where size come into this is that 1/32 of an inch misalignment doesn't impact a large airplane as much as it does a small airplane. Control surface gaps, flying surface alignment, slop in the linkage all add up to have a bigger impact on small airplanes just because the measurements involved add up to a larger percentage of the dimensions of the aircraft and its control throws. You can build a stable, easy flying small airplane but you have to pay closer attention to the tolerances. An airplane with tight tolerances is easier to trim. Another aspect of size and stability is the pilots perception. A larger airplane provides more visual feedback to the pilot. The pilot can perceive and respond to small changes in the aircraft's direction of flight more easily with a larger model. As a result the pilot responds more quickly and with smaller control movements. There is less divergence from the original flight path and thus a perception greater stability even when both the larger and smaller aircraft are capable of flying "hands off" for the same length of time.

In re-reading the original post I think the answer is a lot simpler. When the switch is in beginner mode the little box in the airplane does a lot of the work for you. It can respond more quickly and with more sensitivity than most pilots giving the impression that the airplane is more stable than it would be without the box.