What exactly is a "live" broadcast?

Some shows like American Idol and America's Got Talent are broadcast "live" during finals. But I was wondering. If the show is "live" at 8:00 P.M. EST, wouldn't it have to air at 5:00 P.M. PST? 3:00 P.M. HST? That's inconvenient for the average employee and student. On the other hand, if the shows were filmed live, like The Tonight Show, and simply aired at eight in each time zone, people on the East Coast could spoil the shows by revealing results online or something.