Regarding *super*cooling... Have you ever seen those videos where someone carefully pulls a bottled water out of a freezer which is obviously still liquified, but as soon as they bump the bottle the water instantly freezes? Water can be well below 32F and not be frozen. In fact at my altitude water gets down to about 29F before it freezes naturally. Of course the bottled-water thing can't happen in a pond, but other conditions might make it possible? Realistically though, I think even when you have ice on the pond, the water is usually several degrees warmer, so I think the super-cooling being referenced is from stiring up the water so much that it is all very close to the freezing point through the whole pond... and THAT would be bad for the fish.
Your point about the pumps raises another issue where my pond differs greatly from most others... I have two ponds connected by a stream, and the lower pond (containing the pumps) is quite a bit smaller. The fish stay in the upper pond (which is twice as deep) during the Winter, so the only water moving through the pumps is from the coldest areas, and all the warmer water remains undisturbed.
Your point about the pumps raises another issue where my pond differs greatly from most others... I have two ponds connected by a stream, and the lower pond (containing the pumps) is quite a bit smaller. The fish stay in the upper pond (which is twice as deep) during the Winter, so the only water moving through the pumps is from the coldest areas, and all the warmer water remains undisturbed.