In DC/NVA, they would sound an annoying alarm to get your attention, and run the scroll across the bottom or top of the screen with picture-in-picture technology to show and tell you what's going on. The picture feed would continue.
I've even seen them switch and put your televised program in a smaller screen, but never wipe it out completely.
Similar to politics......five people will say they did good, five will say they did bad, and five won't care either way.