Not true. There are many, many schemes that can be built into the protocol or on top of it to make transactions anonymous. Rather than hastily choosing one, it's probably better to wait for a really good scheme to surface.
Until then, it's opt-in, a hassle, with a small pool of anonymity. But "impossible" isn't the word I'd use to describe the scenario.
So as it stands truly anonymous transactions are impossible. The possibility to make that not true doesn't negate the fact that today bitcoin is in no way a private way of transferring money.
Something doesn't have to be private to be anonymous. So if you're happy with anonymous and public it's possible, but hard.
In the case of the article, the reason it's suspected, not even confirmed, is simply because the number of wallets coins were coming from were identified as the same source.
It's definitely more anonymous than wire transfers, or credit card transactions. The way to avoid detection would be to keep many, relatively small wallets... and disperse money from different sources fairly evently.