I find your faith in the integrity of the US legal system charming.
Bless your hearts.
(see also “use and derivative use” immunity)
Looks like you are right. I was thinking they had to grant total immunity in order to compel testimony, but lo and behold, the “interpreters” of the Constitution strike again:
“In Kastigar v. United States, 406 U.S. 441 (1972), the Supreme Court confronted the issue of which type of immunity, use or transactional, is constitutionally required in order to compel testimony. The Court ruled that the grant of “use and derivative use” immunity is sufficient.”
http://en.wikipedia.org/wiki/Immunity_from_prosecution