for some it's not about introversion/extroversion but simply the fact that whatever part of their brain deals with speech is the same part that deals with thinking through those kinds of problems, so they can't do both at the same time as a matter of physics.
this is to put it precisely. the reality is much messier and varied. the point is, people's brains are not wired the same. and what this means, to make a long story short, is that these interviews are not comparing apples to oranges... not even close.
Coming up with something that works, versus explaining why it works or why you did it that way after the fact.
I think it's the "thinking out loud" part before you have a solution, that can fluster a lot of introverts.