"The main problem is that every transaction is publicly logged. Anyone can see the flow of Bitcoins from address to address (see first image). Alone, this information can't identify anyone because the addresses are just random numbers. However, if any of the addresses in a transaction's past or future can be tied to an actual identity, it might be possible to work from that point and figure out who owns all of the other addresses. This identity information might come from network analysis, surveillance, or just Googling the address. The officially-encouraged practice of using a new address for every transaction is designed to make this attack more difficult."
Not that you are saying they claimed otherwise and it is exactly your article that made me look through this page in detail, so thanks for that.