You are correct

The first use (showing the debate within 10 days of its public broadcast) would be acceptable under Fair Use (according to Guidelines for Off-Air Recording of Broadcast Programming for Educational Purposes, created by a Congressional committee). However, using it beyond that time, unless the copyright holder allows it, is beyond Fair Use. After using it in the classroom within 10 days of its public broadcast, the teacher should either ask permission or pay for a copy of the videotape to continue showing it in his classes.

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