Okay, I do have to agree my response was a bit short.
As noted already, the government has the overall authority to break in on all bandwidths to present emergency broadcasts.
Watching a basketball game and a potential game winning buzzer-beater is in the air? The government doesn't care. They will break in on all frequencies on all stations (OTA TV, cable, radio, etc.) to broadcast an emergency message no matter what else is going on.
Minor, but somewhat interesting information. There was never a channel 1 on original broadcast TV because that was reserved exclusively for government information. I imagine the government still has a reserved frequency, I just don't know if they're still holding on to the original, or if they switched due to the larger bandwidth digital requires.