In GP's example, the "person who owns the database" is already trusted because they wrote the software. The software can insert lies into the blockchain very easily.

I'd also argue that the "person who owns the database" is not just trusted but also trustworthy. They have an incentive to keep lies out of the data.

If the people you can't trust are your users, then blockchain doesn't really add anything. They can insert lies, and you have to verify them. All you get is a guarantee that no one changed their lies to something else.

This is not true. You are always trusting someone. <-- that is a really really big period. In this case you are trusting the authors of the code which this process runs on. The machines that this code runs on. And last but not least the fact that no one has control over majority of the nodes. You are always trusting someone or something.