It wasn't noticed live, the moon was recorded with the help of a telescope and the explosion was noticed later by an analyst.
I also doubt anyone could see that explosion without a telescope as the moon itself is quite bright.
In the video, the narrator says that someone looking at the moon would have seen it, even without a telescope.
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The article says yes, but then quantifies it at 4th magnitude which really isn't that bright. Generally in my area you can't see anything 4th magnitude, nearly ever, due to light pollution. The thought of that right next to even a crescent moon sounds pretty hard to see even in dark skies.
I was going to say the same thing. While 4th magnitude is visible, it's not visible against the background of the already bright lunar surface. The Moon is very bright.