Parenting GameObjects

I have a script that spawns a bunch of game objects (in this case asteroids.) I have tried to create a master "spawn point" game object that acts as the parent for all the asteroids - this way I should be able to just move the spawn point without having to move each asteroid. Here is some psuedo code explaining this:

 void Start(){
 
     public GameObject spawnPointObject = (GameObject)Instantiate(some prefab, some vector, some quaternion);
     
     for (int i = 0; i < 10; i++)
     {
     Vector3 localSpawnPoint = GetRandomPointAroundMe();
     GameObject nextAsteroid = (GameObject)Instantiate(asteroidPreFab, localSpawnPoint, some quaternion);
     nextAsteroid.transform.parent = spawnPointObject.transform;
     }
 }

My problem:

If I do not include the last line "nextAsteroid.transform.parent = spawnPointObject.transform;" all the objects appear around me as they should. If I DO include that line, they all appear on top of eachother - rather that at the vector3's I instantiated them at.

Any ideas?

Edit for additional info:

The spawning script is attached to a sphere that is a child of Camera.main (located at about 0,0,0)

 private Vector3 GetRandomPointAroundMe()
 {
    float randomDistance = Random.Range(5,15);
    Vector3 pointToReturn = Random.onUnitSphere * randomDistance;
    return pointToReturn;
 }