I don't know what BOG is. I do have these helpful links for you:

What are examples of education expenses?

What are qualified education expenses for the American Opportunity and Lifetime Learning credits?

Q. Does the BOG fee waiver count as amount paid to the college?

A.  Simple answer: No.  A fee waver is typically treated as a discount.  

But nothing is simple any more.  If the amount is included in box 5 of the 1098-T, it is treated as a grant applied to fees in box 1.  

BOG - Board of Governors (see https://www.deltacollege.edu/student-services/financial-aid-and-scholarships/types-financial-aid/cal...)