I don't think it's nerves as much as it's a mismatch between someone's internal intelligence/thinking speed and their ability to translate that into speech on the spot.
Yes, absolutely. Different people think in different ways--some in language, some in images, and some even more abstractly. (I suspect this is the key to mathematical talent--whether or not you can think purely in mathematical abstractions without the need of other aid.) So unless you're thinking in language already, there's often a translation process you have to run your thoughts through before saying them, and this process can be expensive, especially with the pressure of people looking at you.