Technically what Ethereum, Bitcoin and Libra are doing are each variations of Byzantine Fault Tolerance based consensus. The key difference is that the former two are permission less and the latter is permissive. Permission less in this case means that anyone can start a validator node and verify transactions this typically involves either proof of work or stake. Permissive means that only some validators are able to do that and that the consensus is based on verified identity: each validator has a known identity and only explicitly trusts certain other well known validators.
As the article nodes, it would be a mistake to assume that that is only Facebook. What Libra does is actually similar to Stellar and Ripple, which are also based on permissive BFTs.
Since I've used Stellar, I know a bit more about how that is structured. In short, in Stellar, anyone can start a validator and start validating transactions. This is commonly done by people with a need to validate transactions for scaling reasons. Every validator is configured with a list of other validators that they trust and a consensus quorum that needs to be reached between those for a transaction to be acceptable.
The flip side is that for your transactions to be acceptable to others, they'd have to trust you. In practice these sort of bi-directional trust relations only happen on a need to have basis; for example because you and your business relations are swapping the same tokens with each other and have a business need to trust each other's work. The extended network of mutually trusting validators that trust each other directly or indirectly is the basis for the consensus. After some incidents with the Stellar network halting its consensus, Stellar is actually moving to reduce the reliance of the network on their own validators. The recent outage in May was actually root caused by several non SDF owned validators going down. This sounds bad but it is actually a safety feature: stellar will prefer partition tolerance and consistency over availability. Ethereum and Bitcoin have had issues with favoring availability over consistency. If you are running a bank, that is kind of a big deal.
Libra is launching with a quite broad consortium that each will run validators. I imagine that like in Stellar, each of those validators will eventually be able to start trusting other validators at their own discretion. I'm assuming that that is what Facebook means when they say they will eventually open up.
It seems like initially this will be tied to deals with Calibra, which is a subsidiary of Facebook and which is responsible for hosting the reserve that backs the Libra, and other stable coins that will be running on the network. A key difference with Stellar, which is run and controlled by a foundation representing its members, Calibra is instead a commercial entity owned by Facebook. Presumably the consortium members have some kind of contractual agreement with Calibra about this. In other words, Facebook as a owner of Calibra is a bit more special than everyone else. I imagine they also hold patents, trademarks, etc. as well. To be clear, the software itself is Apache licensed.
Like many, I wrote up my own thoughts on Libra and wrote a lengthty article. You may find it here: https://dev.to/jillesvangurp/libra-blockchains-and-the-meani...
In short, what they are doing makes sense practically, technically, and legally. People are obviously talking a lot about legislation currently and Facebook's motivations. My impression is that governments are mostly still applying and interpreting existing laws when it comes to blockchains and are actually quite slow in responding in a coherent and timely fashion with new laws. My guess is that Facebook and others are counting on this and are looking to create a financial reality where shutting this down becomes economically more difficult. In short, once they are moving lots of money around, shutting them down becomes impractical.