The IRS allows you to move around how the scholarship was used. If you claimed it went to room and board rather than tuition, you would have spent more on tuition. The student has to claim the small difference as income and may be subject to the kiddie tax but it is usually well worth it for the parent to claim the education credit.
The IRS has a great brochure that explains how scholarships and tax credits interact.
You can use the IRS’s Interactive Tax Assistant tool to help determine if you’re eligible for educational credits or deductions, including the American Opportunity Tax Credit (AOTC) or the Lifetime Learning Credit (LLC).
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Reference: What is the Kiddie Tax?
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