This is true and massive mistake on the reporters part.
However the overall concept of the article could be easily applied to coins such as Zcash and Monero that do have anonymous transaction methods.
In my comment [1] I argue that even then, these types of trades are not a concern for the IRS.
Why would you do this? Why would anybody ever accept a private key in a transaction. Now the key is no longer private!
When reading articles like this I substitute "Bitcoin" for "Cryptocurrency" and it makes more sense. The public has just recently normalized Bitcoin and so that's what they write about. Give it a year or so and they'll catch on.
I get what you're saying, and I've been saying the same myself. Then again, maybe it is anonymous in the literal sense that transactions don't include your name. Without outside information, you can't look at a transaction, or a history of transactions, and tell to whom they belong.
PS: Never mind. I don't think I am making an important point.
In practice, this means that if you use coinbase, or any large web merchant, that merchant can link your identity to the wallet you use, and then to almost every other transaction you spend.
The bitcoin UTXO transaction graph adds in some anonymity, because it's hard to be sure which part of a transaction's output is going to the merchant, and which is coming back to the user in the form of change. However, in practice, forensics are quite good, and are certainly good enough for the government (if they hired any decent tech person) to figure out.
On the other hand, coins like Zcash and Monero are anonymous, and the IRS might have reason to actually fear those.