Not communicating enough info to rebuild the tree is a separate issue, but it is mentioned in the article so the reader is not left guessing. In the example however, we have a set of 6 symbols that would require 3 bits each to represent uncompressed but instead assume 8 bits. It invites fairness questions, which would distract a reader that has not been exposed to the concept before. This is an otherwise nice intro to the topic though.