The mistake was so trivial it doesn't even matter. Si-Hyun is the absolute leader of the organisation, or at least she should be, so it's her responsibility if an underling makes a mistake. Whether she ordered the destruction of Paeng family personally or not is irrelevant. Her job is to make sure her sect does nothing that goes against her plans. She clearly isn't going that because she allows the folks under her to do whatever they want. Afterwards she barely bothers to admonish them, as if that made any difference since we are talking about villains who only obey power.
That being said, the author is doing pretty good job at depicting Woo-Moon as inexperienced, because that's what he is. I feel like he's going a bit over the top, though, exaggerating Woo-Moon's naivety too much.