From the information you are providing in your post, you technically have not 'graduated' from the school if you have not passed an important test that they require you to complete. As a part of their policy, they are not obligated to give you any type of certificate of completion(release of information?) until you satisfy that portion.
I don't see anything illegal about it. Simply, you did not complete the program(that portion anyway, the extra test prep step), therefore, you are not qualified to sit for the NCLEX according to them and even the state's BON since you do not have a certificate of completion(release of information?). The school has to adhere to the policies of the state BON.
I suggest you abide by their suggestion. Use that month of study to really improve yourself. Don't just try and meet the percentage they require for you to pass, but go above and beyond it. It can only help you when you sit for the NCLEX and improve your chances on passing it, since I am sure the test you are taking (I am considering it might be the HESI?) is closely related to the NCLEX.
Best of luck.