Pub 970 page 21 addresses this. The verbiage differs from mine but the effect is the same. I believe the intent is to prevent wealthy parents whose income limits the credit from getting the advantage of their student getting the refundable credit by not claiming the student.
Refundable Part of Credit
Forty percent of the American opportunity credit is refund- able for most taxpayers. However, if you were under age 24 at the end of 2019 and the conditions listed below ap- ply to you, you can't claim any part of the American op- portunity credit as a refundable credit on your tax return. Instead, your allowed credit (figured on Form 8863, Part II) will be used to reduce your tax as a nonrefundable credit only.
You don't qualify for a refund if items 1 (a, b, or c), 2, and 3 below apply to you.
1. You were:
a. Under age 18 at the end of 2019, or
b. Age 18 at the end of 2019 and your earned in- come (defined below) was less than one-half of your support (defined below), or
c. Over age 18 and under age 24 at the end of 2019 and a full-time student (defined below) and your earned income (defined below) was less than one-half of your support (defined below).
2. At least one of your parents was alive at the end of 2019.
3. You are filing a return as single, head of household, qualifying widow(er), or married filing separately for 2019.
