The Supreme Court has ruled that executive privilege is part of being president. However, executive privilege is limited.
The Supreme Court case that ruled on this was US vs. Nixon. During this time, Richard Nixon was being put on trial for his possible ties to the Watergate scandal. When this issue was brought to court, the courts demanded phone conversations that were taped from the president. However, Nixon said that he did not have to give up these tapes because they were part of his "executive privilege." The Supreme Court did not agree with Nixon.
The Supreme Court ruled that nobody is above the law and that presidents cannot use this idea to simply escape punishment.
the responsibility of the DHS would be to identify when and where the attack occurred, and they also have the job to hunt down the person who planned and committed the attack