Hello and thank you for your question.
Yes, but it wouldn't do much good and it's still better for the parents to claim their son. The son won't owe any tax with that income and the refundable portion of the American Opportunity Credit won't be available to the son so the credit is worthless.
See IRC 25A(i)(5), (emphasis mine):
(5) Portion of credit made refundable
40 percent of so much of the credit allowed under subsection (a) as is attributable to the Hope Scholarship Credit (determined after application of paragraph (4) and without regard to this paragraph and section 26(a)) shall be treated as a credit allowable under subpart C (and not allowed under subsection (a)). The preceding sentence shall not apply to any taxpayer for any taxable year if such taxpayer is a child to whom subsection (g) of section 1 applies for such taxable year.
Fast-forward to IRC 1(g), regarding the so-called kiddie-tax:
(g) Certain unearned income of children taxed as if parent’s income
(2) Child to whom subsection applies
This subsection shall apply to any child for any taxable year if—
(A) such child—
has attained age 18 before the close of the taxable year and meets the age requirements of section 152(c)(3) (determined without regard to subparagraph (B) thereof), and
whose earned income (as defined in section 911(d)(2)) for such taxable year does not exceed one-half of the amount of the individual’s support (within the meaning of section 152(c)(1)(D) after the application of section 152(f)(5) (without regard to subparagraph (A) thereof)) for such taxable year,
In short, since the child's earned income doesn't exceed one-half of his support and the child meets the age requirements of IRC 152(c)(3) because he is a student under the age of 24, IRC 1(g) applies to the child and the child does not receive any refundable American Opportunity Credit under IRC 25A(i)(5). The non-refundable portion of the American Opportunity Credit would only serve to offset the child's tax, which is $0. There is no benefit, therefore, for the child to claim the American Opportunity Credit. At least if the parent's claim the child they'll get to make some use of the exemption for a dependent.
I hope this was helpful.