A public ledger does not mean that everyone can see what is on that ledger, that's the beauty of Blockchain, although for some blockchains such as Bitcoin you can see what is on the ledger. For a blockchain that does allow truly anonymous transactions, see eg Zcash. Zero knowledge proofs are used to achieve anonymity.
I wrote the article at a general level to explain Blockchain to people who don't have a technical background in Blockchain. Given the word length, hard to go into technical details. Also, the technology is moving so fast that what was considered impossible is now being worked on.
Bitcoin is comparative slow and clunky, some other cryptocurrencies are lot faster. But saying that I've used Bitcoin a number of times in the past month or so and all the transactions have gone through just fine.