Q. The box noting if hard copy was mailed was checked No. Does that mean the school didn't send the 1098-T and if not, is the credit not allowed?
A. No. You are allowed the credit. A copy of the 1098-T, printed from the school's web site counts as having received a 1098-T. You have a 1098-T that qualifies for the credit.
Yes, a 1098-T is required to claim the credit, but exceptions apply. In your case, you don't need an exception because you have a qualified1098-T.