If the student is the parent's dependent, the parent is the only one who can claim a tuition credit. Since that is the usual situation, usually only the parent enters the 1098-T.
If a portion of the student's scholarship is taxable, the student will also have to enter the 1098-T to properly account for the taxable scholarship. If the student takes a distribution from a 529 plan, he may have to enter the 1098-T to account for expenses and calculate the taxable portion of the distribution (if any).
There are three things you can do with your Qualified educational expenses (QEE):
Allocate then to scholarships (so that the scholarship remains tax free)
Use them to claim an education credit
Allocate them to the 529 distribution (1099-Q) so that it will not all be taxable
You are allowed some leeway, in how you allocate QEE, for the best tax benefit.