Yes, that's correct.  IRS publication 970 (https://www.irs.gov/pub/irs-pdf/p970.pdf) states on page 11:

Generally, you can claim the American opportunity credit if all three of the following requirements are met.

• You pay qualified education expenses of higher education.
• You pay the education expenses for an eligible student.
• The eligible student is either yourself, your spouse, or a dependent you claim on your tax return.

Note. Qualified education expenses paid by a dependent you claim on your tax return, or by a third party for that dependent, are considered paid by you.