When a witness is granted use immunity, can he refuse to testify on the grounds of his Fifth Amendment privilege against self-incrimination?

When a witness is granted use immunity pursuant to 18 U.S.C. Secs. 6002 and 6003, ordinarily he may not refuse to testify on the ground of his Fifth Amendment privilege against self-incrimination, since he is protected against the direct or derivative use of such testimony against him in any subsequent federal or state prosecution. Kastigar v. United States, 406 U.S. 441, 459, 462 (1972). Such use immunity "affords the same protection [as the Fifth Amendment privilege] by assuring that the compelled testimony can in no way lead to the infliction of criminal penalties." Id. at 461. Such immunity "is coextensive with the privilege and suffices to supplant it." Id. at 462.