The question of whether or not a president can suspend habeas corpus has not been determined. And that is not only my opinion, but the considered opinion of the current Chief Justice as well.
Sure it has. That only Congress could suspend it was the unanimous position of the founding fathers. If you dispute this quote me one who says otherwise.
That only Congress can suspend it is also the standing court ruling on the only two cases to render a decision on a president who did it: In Re MacDonald of the U.S. District Court in St. Louis and Ex Parte Merryman of the U.S. Court of Appeals in Baltimore. Both of them were against Lincoln.
And that is not only my opinion, but the considered opinion of the current Chief Justice as well.
All facts considered, the current Chief Justice is simply wrong.