I don't understand why they're proposed as a solution to this type of problem at all. I'm a big fan of blockchains, I work for a company/project completely reliant on them, but I don't get where people think they'll be useful for things like credit monitor and health care records. It makes no sense to me.
Just to play devil's advocate, since I don't think they are a good solution either. Unlike healthcare I think you could use some of the properties of a blockchain to help reduce the risk of leaking personal information during credit checks. For example: you could prove your identity by making a transaction and then show a timely series of past payments.
(If you're not laughing then you need to admit you have a problem)