But what people really argue for is that it makes the system much less prone to corruption and manipulation, because the system of tracking is much more resilient to being tempered with.
For example, right now Joe Shmoe could fabricate a fake paper deed showing that his great grandma owned the Mona Lisa, and it is thus his. And then sue the French government saying they need to either buy it off him or return it to him. Now you'd need forensic experts and all to try and check the authenticity of that deed and all that.
Now this is a bit of a stupid example obviously. What if the deed was real? Would the government still say well oh crap here you go? I guess that will depend on the French government and their laws.
But say the laws of France were such that yes, it should indeed therefore be returned to Joe.
Well with blockchain, the idea is that this wouldn't happen. First the "deed" would have never been lost, the ledger tells you who owns what, there'd be no confusion. Second, Joe (if he was lying), wouldn't be able to create a "fake" entry in the ledger as easily as maybe he can fabricate a deed. Now that's up for debate, but in theory a decentralized ledger need you to temper with all the nodes, so it's possibly much more difficult to scam with.
And back to the example in the article, the Mona Lisa would be transfered from the government to Joe, there'd be a record of this. Now the question is no longer, is this record valid? We know this happened, the question becomes was this transaction initiated fradulently? Obviously the computer doesn't know why the transaction came to be, just that it for sure did, not tempered with, no fake claims, this did happen and we know exactly from where and to where, and exactly what was it that was transacted.
Now you need people to investigate and asses if the transaction was fraudulent. Until there's a way for machines to with 100% accuracy read intent, this has to be handled by people. But in theory, a decentralized blockchain might make that process easier and more resilient to scams.