In our organisation, taking an exam is not a right, it's a privilege. You can apply to take the exam, but whether you take it or not is not up to you. Admittedly there have been very few cases where people have been told not to take the exam, but it has happened. How they deal with that is one way their character can be assessed, how people deal with failing exams is another. As to going to other Dojos to take their exams, that would go down very very badly and is a sure sign of "belt chasing".