Instantiated bullet moves relative to original object?

I have a simple “shooter” component attached to my main character; let’s call him Cube Boy. Cube Boy fires a tiny cube whenever you press space. However, when you move Cube Boy while the bullet is still visible, the bullet moves relative to Cube Boy - not independently as you would expect. What’s going on?

Here’s the script attached to Cube Boy:

public class CubeShooter : MonoBehaviour {
	public Rigidbody bullet;
	public float speed = 10.0f;

	void Start () {}
	void Update () {
		if (Input.GetButtonDown("Fire1")) {
	void FireBullet() {
		Rigidbody bulletClone = (Rigidbody) Instantiate(bullet, transform.position, transform.rotation);
		bulletClone.velocity = transform.forward * speed;

The behaviour you describe would happen if your bulletClone was a child of Cube boy. I don’t see anything here that makes it a child, so look at any script attached to the bulletClone.