Rso: I was busy until now, but here’s a possible explanation is that the sundial was poorly constructed.
Sundials work because of the contrast between the shade and the dial, so if the sundial is made of a dark material, and there’s too much external shade, the contrast will be mush lower, and the sundial won’t work.
So what would the tree do?
When sun goes through a tree, some rays get blocked by leaves. Some rays go through the leaves, and some rays go between the leaves.
So when you’re on the ground, you’ll see the sun, but it’ll be slightly darkened. So the scientists said like you “you see the see the sun. So obviously nothing’s blocking it.” While the Alter Rebbe said that while it’s not blocked completely, it’s blocked enough to break the sundial.
But even leshitosecha, it still could be that the Frierdiker Rebbe heard the story the way he wrote it, and his mistake was that he was too trusting, and there was some kind of broken telephone somewhere up the chain.