I agree with you 100%. Everything I read online says or implies that if box 5 exceeds box 1 then you have taxable income. Say someone has a 100% tuition scholarship. In that case there would never be a box 1 amount and box 5 would be the annual tuition. That makes no sense (dangerous words). I also noticed the "deemed" wording. However, I could not track down a definition of "deemed". The other argument in favor of your conclusion is the definition of a non-taxable scholarship (IRS website Tax Topic 421):

If you receive a scholarship, a fellowship grant, or other grant, all or part of the amounts you receive may be tax-free. Scholarships, fellowship grants, and other grants are tax-free if you meet the following conditions:

• You're a candidate for a degree at an educational institution that maintains a regular faculty and curriculum and normally has a regularly enrolled body of students in attendance at the place where it carries on its educational activities; and
• The amounts you receive are used to pay for tuition and fees required for enrollment or attendance at the educational institution, or for fees, books, supplies, and equipment required for courses at the educational institution.

Per Pub 970: Qualified education expenses. For purposes of tax-free scholarships and fellowship grants, these are expenses for:

     • Tuition and fees required to enroll at or attend an eligible educational institution; and
     • Course-related expenses, such as fees, books, supplies, and equipment that are required for the   courses at the eligible educational institution. These items must be required of all students in your course of instruction.

Lastly, worksheet 1 in Pub 970 does not reference form 1098T. It only refers to Scholarships and Qualified educations expenses. Nowhere in this section of publication 970 or on the worksheet does it say "amounts paid" when referencing qualified education expenses.

I have a similar situation as yours with my daughter. My initial approach was to bite the bullet and report the excess of box 5 over 1 as income (and Box 1 was an incorrect amount). But the scholarship could only be used for tuition i.e. a qualified education expense. Therefore, it meets the definition of tax-free. I will consider the scholarship non-taxable. This may require some adjustments when reporting the 1098T in different tax software programs.