I feel like there are a lot of reasonable and unreasonable claims about blockchain and cryptocurrency, but the biggest problem is that people don't understand the technology. I think it's important to look at what blockchain is, what it isn't, and why people say it can do things that it can't (or shouldn't).
Blockchain is a distributed ledger. It's a database that everyone has access to, but no one can edit (at least not without consensus from all participants). That means that if you create something on the blockchain, you own it—no matter who tries to change it or delete it. And when I say "everyone" has access to this database… I mean EVERYONE! That includes your grandma and even my dog.