Yes, if the 1099 is for an education distribution, it would be a 1099-Q. (a 1099-G is usually a tax refund, unemployment or some other government payment). But the bottom line is yes, you are right. If you enter the forms on the student's return so that the distribution is not taxed, and the result also includes that the credits are not taken, it is fine. There is no credit and no tax due on the distribution.
