When it comes to issues like this one I just chalk it up to divine intervention and move on. House was there because the show needed him to be there. If he hadn't been there wouldn't have been an episode. If Cuddy hadn't been there, ditto --and really, why was she? She's a desk jockey. There's no way a Dean is crawling around an accident site unless it's a dire all-hands-on-deck kind of thing...and this wasn't, which is why she had Wilson at PPTH and sent another doctor (Foreman?) back with a patient. So again, it's back to meta. They were there because the writers decreed that they be there.

Anyway, in these kinds of things I resort to meta and just give Cuddy a pass here. House's presence on site is ridiculous, his crawling around in the rubble is ridiculous,and Cuddy telling him he had to stay was ridiculous. But up until the last 5 minutes it was an amazing episode. You can't judge TV characters as if they were real people because they aren't. Their actions will be inconsistent not because they are harboring darkness and secret agendas, but because they are written by people who make them behave in such a way as to advance the plot of the moment.

There are things I disliked about Cuddy in this episode, but House being at the site wasn't among them.