There's a loop hole available. The student declares another $4000 of scholarship (or at least $2000)* to be taxable, that way the parent can use that much tuition to claim the Credit. You cannot use the loop hole if the student's scholarship is "restricted" (that is it must be used for tuition). Most scholarships are not restricted (the schools are aware of the "loop hole").
*For the American Opportunity credit, the first $2000 of tuition gets a 100% credit ($2000 tuition paid = $2000 Credit). The next $2000 gets a 25% credit.
