It’s called simulcasting. Fox records the debate moments before it is aired not-quite-live. There is a small delay, and it is recoreded as it is broadcast, thus “fixing” it in a “medium,” — the requisite for copyright protection.
It's called a loophole. One that ought to be plugged for any broadcast of a political debate or a political event.
The people of the United States of America own the airwaves, not Fox News. The copyright law that supposedly protects Fox's alleged right to the "rights" to rebroadcasting this event is legislative and not constitutional. Congress should send a message to these networks that overreaching will not be tolerated. They should pass emergency legislation revoking any copyright protection to any broadcast of a political debate.
Now perhaps you can point me to the law that supposedly gives Fox a copyright to the broadcast of a presidential debate. Everybody seems to know there is one, but nobody seems to know the citation. I suspect it is contained in a judical opinion somewhere and is not a specific delineated legislative right.