If the candidate would like some quiet time to think about the solution, I expect them to respond with "I think I'm forming a solution, just give me a couple of minutes to think about it before I present my case".

If they can't even do that, then I'm sorry, but they are no good to anyone. You can be the smartest and best developer in the world, but if you're completely incapable of representing yourself and your ideas; to have a dialog about your work, you are effectively worthless as an employee.

Some companies might have a place for that special someone, who you can lock in a room for a month and he will later emerge with an amazing new piece of code that will solve your problems, shielded from all the problems of the outside world, but companies where that is possible are very rare.