Yes, your suspicion is true. The ALL_OBJECTS view will list only those items that the current user has access to.
If you can log in as USER2, you can request USER_OBJECTS as this user to view all objects belonging to this user.
If you can log in as SYSTEM, you will have access to all objects regardless of the owner, so the list provided by ALL_OBJECTS (or DBA_OBJECTS) will be completed.
If you cannot log in as a user with access to all USER2 objects, then you cannot list all USER2 objects.
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