In a semi-lattice, such overlaps are possible, though of course, hierarchies are a subset of semi-lattices. It's the distinction that Alexander is interested in. Alexander then goes on to show how many designs for cities and many new cities (including Brasilia) are in fact trees.
Alexander then suggests that hierarchical thinking is hard for designers and planners to avoid because of a human psychological predispositions to use hierarchies or order and remember things. But, he argues, it's impossible to get a hierarchical decomposition that captures all the associations between elements, so attempting a hierarchical organization leads to the cutting of essential links in people's lives. His beautiful, furiously rhetorical last paragraph :
For the human mind, the tree is the easiest vehicle for complex thoughts. But the city is not, cannot and must not be a tree. The city is a receptacle for life. If the receptacle severs the overlap of the strands of life within it, because it is a tree, it will be like a bowl full of razor blades on edge, ready to cut up whatever is entrusted to it. In such a receptacle life will be cut to pieces. If we make cities which are trees, they will cut our life within to pieces.
Of course, it immedietely suggests :