It's very useful when `pub` is equivalent to "this is crate's public
API", let's enforce this!
Ideally, we should enforce it for local `cargo test`, and only during
CI, but that needs https://github.com/rust-lang/cargo/issues/5034.
This seems like a better factoring logically; ideally, clients shouldn't touch
`set_` methods of the database directly. Additionally, I think this
should remove the unfortunate duplication in fixture code.
