Huckabee is ignorant. Hogan sued Gawker for invasion of privacy.
Cruz cannot sue NE for libel based on incorrect, harmful allegations that damaged his reputation. He is a public figure. To prevail in a libel case, Cruz would have to prove that NE acted with malice and knew the allegations to be false.
bingo!
Hogan won an invasion of privacy action.
If Cruz had any cause of action it would be defamation, and public figures have such a burden to make, it is very seldom worth the effort. Even if it were, if he filed yesterday it would not be resolved until after the election. So in neither event would it be worth his time at this critical point in the campaign to dedicate resources in that direction.