It is not just Fox but many media outlets who can selectively edit, clip and frame what you see and thereby shape a narrative and a sense of reality that is different from that which is experienced, in this instance, in the studio itself.
I am reminded of the famous saying in Russia during the Soviet period. There were two main organs for news run by the state; Pravda and Izvestia. Pravda meant "truth" and Izvestia meant "news". The Russians had a pithy running joke that is lost in translation but ran along the lines of there is no truth (pravda) in news (isvestia) and no news (isvestia) in truth (pravda).