Not really true. Kiwi birds are very furry (unless you define furry as having mammalian hair, which sort of defeats the point) and are more related to lizards than to mammals.
Well, I suppose the more striking statement is that you can find two trees and two bushes such that there is a tree/bush pair that is closer related than the tree/tree pair.
I think visually the first two look alike and the last two look alike. I would phenotypically bucket them together. But the reality of genetic relation is different.
Well no, 2 randomly selected trees for the same species are quite likely to have a recent common ancestor (contrasted with, say, a tree and fish) because they're the same species.
I was under the mistaken impression that "tree" was a phylogenetic thing. Like, they're all descended from some distant great-grandmother-tree or something. The surprising thing was that this is not the case, and many separate species have all discovered how to tree individually.
Otherwise that statement is not surprising at all.