Correcting minor errors of fact "live" is neither possible nor desirable, but a willingness to say "no, that's not true" to ridiculous lies that you can predict in advance instead of just letting them go by is good!
Journalists often act as if there isn't a meaningful difference between a minor exaggeration or flubbed fact and the nonsense Trump (and other politicians) often spews , or that this difference isn't important, but they're just pretending not to understand things they do understand.