Knowing how live TV works and how much of a circus the control room can be, where everything is about hitting marks and staying on schedule, it likely went over everyone's head. That's also likely why Braden didn't react at all while standing next to him: he had someone chattering in his earpiece the entire time. Kuiper could have been talking about engaging in a cocaine-fueled orgy the previous evening (which would have been preferable to what he actually said), and as long as he said in a measured tone with a regular cadence and didn't go over-time, nobody there would have reacted.

The producers probably found out about it when everyone else did: When someone posted a clip on Twitter.