Like every good tale, there is some truth to it. The Joint Special Operations Command, or JSOC, does participate in the black operations hunt for al Qaeda and other terrorist groups' leaders. This is done in conjunction with the CIA's Special Activities Division. There is little secrecy about this, just read Jawbreaker or this article by Bob Woodward from back in November of 2001.
But to claim that JSOC does not "report to anybody, except in the Bush-Cheney days, they reported directly to the Cheney office," or that "Congress has no oversight of it" is just false. JSOC was established in 1980 after the failed mission to rescue the hostages at the U.S. embassy in Iran. JSOC is a component command of the U.S. Special Operations Command, which reports to the Secretary of Defense. JSOC, like the CIA, certainly falls under congressional oversight.
Hersh has made a living of making fantastic claims that don't quite live up to the hype. Chalk this one up as another Hersh fantasy.