If he is an extrovert then why only three people? Why the same three people? Why shun new people or changes to his environment? Why is he so sure he's right? Why doesn't he evade incoming criticism? Surely it is INTJ to just stand there as if all the bullets and tank shells in the world could not pierce his defences?
I'm not sold but you make an interesting counter point.
Perhaps if we analyse in what way House is messed up then we would be able to remove this and see the creature underneath (this is way too in depth for a TV character but it's fun ).