Confusion over namespaces in doc comment tests

Question

Very new to Rust, and I've run into an issue with trying to get doc comment tests working.

I'm hoping to have a module that isn't public, but has some tests in the doc comments.

src/lib.rs:

pub mod module;

fn foo() {
    println!("{}", module::get_hello());
}

src/module.rs:

/// Gets a nice Hello message
///
/// ```
/// use test_namespace::module::get_hello;
/// let msg = get_hello();
/// assert_eq!(msg, "Hello, World!".to_string());
/// ```
pub fn get_hello() -> String {
    "Hello, World!".to_string()
}

The only way I've been able to get this test working is if I have pub mod module;. I feel like there should be some way of running this test without the use test_namespace::module::get_hello; at all since it's a test in the same module. Hoping to get some clarification.