There were some reporters arrested and detained for a time, but these were mostly in the border states and acting as propogandists for the Confederacy. For a while the Chicago Tribune was shut down, but that was the action of Gen. Rosencrans and not Abe Lincoln. I haven't heard anything about reporters being held in a warship, likely that's the radio host mistaking U.S. POW's from the Revolutionary War with prisoners in the Civil War. There wouldn't really be a reason to hold prisoners in a warship since there were plenty of prisons and prison camps that they could have been sent to.
SOME of the PRINTERS/EDITORS/REPORTERS were kept in that "big hole in the ground" for 2 years, WITHOUT warrant, charges,indictments or even the pretense of a trial, according to the official US Army guide at Ft McHenry.
other members of the "Fourth Estate" were transferred to confinement at Point Lookout DEATH Camp, to Camp Douglas or to Elmira (HELLmira), NY for "preventive detention" and/or for punishment WITHOUT trial, until their death or the end of the war. (MANY perished at those DAMNyankee HELLholes of abuse,torture,intentional starvation,exposure to the weather & by denial of clothing/medical care! SOME members of the press were simply MURDERED, as it was easier & "more convenient" than confining them.)
free dixie,sw