Loose Lips Sink Ships was itself an information management scheme to avoid informing the public.
The Germans didn't have spies collecting rumors in the US. Nor did they need them during Operation Drumbeat (the U-Boat attack on the US coast). The US was completely unprepared for Drumbeat. They had no harbor defenses, no convoys, inadequate and unprepared coastwatcher and patrol services.
The point of the censorship is to not cause panic among the public as they realized how badly the US was losing. Drumbeat was worse for the US than the attack on Pearl Harbor was, both in terms of lost ships and number of Americans killed. It was about controlling embarrassment for the Navy. American ships were blowing up and sinking within eyesight of shore. Vacationers were finding dead seaman washed up on the beaches of Florida and New Jersey. The military did not want these events turning into major media events.
And to the extent that the censorship was justified, yes, at the very least we were legally in a properly declared war.
Ironically, there was one time the media did cause a massive problem that could have affected the outcome of the war.
The Chicago Tribune sent a reporter to Pearl Harbor after the battle of Midway and managed to learn from some indiscreet senior commanders that we knew where the Japanese fleet was because we cracked their codes.
The reporter published the story in the Tribune. It was pure dumb luck that the Japanese never noticed the story. Roosevelt wanted the reporter and Robert McCormick brought up on espionage charges, but Admiral King asked him not to prosecute because the Japanese didn't seem to notice the article but they'd definitely notice the trial.
Germany not only had spies, there were multiple (albeit failed/foiled) sabotage attempts by Germany on US soil.
Part of the issue the US had is the very large (significant percent of the population) 1st gen German immigrant population. There were concerns they would sympathize.
What was actually happening is many of these immigrants were there to get away from Hitler and Germany as it was at the time, so Germany found most of its attempts stymied instead. But they did try.
>The Germans didn't have spies collecting rumors in the US.
Yes they did. https://en.wikipedia.org/wiki/Duquesne_Spy_Ring