If it's a live broadcast, they aren't using film - they'd be recording either to analog videotape or (more and more often these days) to a digital medium of some sort, which either way will be 60 cycles per second.

This actually brings up one of the long-standing challenges encountered by progressive scan DVD players when deinterlacing - some material started life at 24fps and some (such as many, but not all, TV shows on DVD) started life at 60fps. The DVD format provides flags for identifying the video's origin, but the flags aren't always right (hence problems with "flag-reading" progressive scan players).