If a person qualifies to be claimed as a dependent, they must answer "yes, I can be claimed as a dependent", even if the person who could claim them, agrees not to. Answering "no, I can't be claimed" in order to qualify for a rebate may be considered tax fraud, although we don't know yet how efficient the IRS will be at auditing such issues. The IRS has 3 years to audit normal returns, and 6 years in the event of deliberate fraud.
There is a second question, "will the person who could claim you actually claim you". This only relates to the claiming of the American Opportunity Credit. In some cases, if the student has income earned from working and the parent's income is too high to claim the full AOC, it may be to overall advantage for the parents to decline to claim the child and the child to claim the AOC. But the child/student must still answer "yes" to the first question.
