The muscles get stressed due to lack of fuel and the metabolism of fats kicks in, ketones start being produced and the danger of ketosis or ketoacidosis looms. This is the basis for another rule of thumb which is often misunderstood. Exercise in those circumstances will make things worse, not better. Why your bg is elevated is just as important as the fact of the elevated level when deciding whether or not exercise is contraindicated. The 240 is also a somewhat arbitrary number.
Some people start throwing ketones at significantly lower levels.
Do exercise if you are sure your insulin level is adequate but your blood glucose is too high. Exercise also produces effects at longer time scales. Sometime after exercise, there is often a take up of blood glucose by the muscles to replenish depleted stores. Again, as is the case during exercise, artificially high insulin levels will lead to hypoglycemia. The last rule of thumb is to watch for hypoglycemia after exercise.