Tim Swanson is neither a developer nor an academic researcher. He writes fairly good summary articles where he quotes other people and offers some common sense-based analysis, but lacks technical understanding and rigor to do original research.
I described anchored sidechains back in 2013. It can be demonstrated that if you do it right, it is exactly as secure as Bitcoin itself.
Newspaper vs blockchain: If you want to use anchoring as a consensus mechanism, you need a programmatically-accessible data source, such as a blockchain. Publishing the hash in a newspaper is cute but will have to rely on manual entry. A copy of a newspaper can be faked. How do you know that one you have in your hands has the same hash as the ones which are held by others?
does not fully reduce the risk of a well-funded attacker trying to revise history.
Nothing is 100% foolproof. But if an attacker has to spend $500M to try to revise history, that's a good deterrent.
If you only have copies of the blockchain on computers you control and it's not anchored anywhere, it's possible to mount an attack without paying anything. E.g. suppose that a private blockchain is hosted on 5 servers, and one system administrator has access to all of them. Then hijacking that administrator's computer is equivalent to getting a complete control over the private blockchain, and it will allow attacker to rewrite history. Hijacking computers is often done cheaply using social engineering or widely available malware. (E.g. read about BitStamp hack.)
If you anchor your blockchain in the Bitcoin blockchain, there is no shortcut: you have to spend a lot of money to rewrite history.
One thing which Swanson fails to understand is that one can combine multiple security mechanisms.
If you just blindly rely on Bitcoin blockchain, you might get into a trouble: somebody might actually spend $500M on mining hardware to steal many billions worth of assets.
But anchoring can be trivially combined with trusted hardware protection and legal protection. You just require those hashes to be signed by your private blockchain nodes, and now an attacker has to BOTH hijack your servers AND to attack Bitcoin blockchain at the same time. So it's strictly MORE expensive to mount an attack.
As for legal protection, of course, you won't just say "OK dude, you hijacked our servers and rewrote Bitcoin blockchain, you win, those assets are yours". There will exist hard cryptographic evidence that transaction history was rewritten in a particular way, and it will probably incriminate a particular group of people. So they will go to jail and the history will be corrected via a hard fork.
So, basically, to steal assets attacker will have to:
Great plan!
So what's the role of anchoring in this? It's a great deterrent. It will cost you maybe $10 per year, but it means that attacker will have to spend millions of dollars to even try. It's a great deal, if you ask me.