Not understand exchanging argument proof for optimal prefix code
What Kleinberg and Tardos show is that given a tree $T$ containing a node with a single child, they can come up with a strictly better tree $T'$, showing that $T$ isn't optimal. Therefore an optimal tree cannot have a node with a single child. Whether this qualifies as an exchange argument or not is not so important.

More generally, the form of the argument is "if X doesn't satisfy P then X is not optimal; hence any optimal X satisfies P". In order to show that X not satisfying P cannot be optimal, they modify X to obtain a better X'. This is a common enough pattern which doesn't usually have a name attached to it.