Student Worksheet Part VI line 20 deducts scholarship received in line 15 from expenses paid in line 1, which is already net of scholarships. What have we done wrong?

Look at the amounts in Box 1 and 5 on your 1098-T.  The box 1 amount is before the deduction of scholarships received. 

The box 1 amount IS the amount I paid to the institution.  It was after Scholarships.

For an example, Box 1 show $5,000 - the amount I paid out of pocket, Box 2 is blank, box 5 shows $3,000.  Part VI say my adjusted expenses are $2,000 when I am out of pocket $5,000.