It could be that, considering where they were going and what they were doing, that the mission was kept secret. Plus he was killed by a child, in a time like that people likely wouldn't believe it, or they'd just be in total shock that it could possibly happen, which could cause problems. And If the Commando that died had no family, word likely didn't get out that he passed.
It could also be that the announcer was implying the missions the commandos did with Cap, and how Bucky was the only one to supposedly die in that time. I dunno D;
Perhaps we'll get more information/explanation in the next episode?