The Form 8863 instructions are referring to whether or not you are a dependent of your parents. It does not impact your eligibility for the AOTC, it only determines whether it will be you or your parents who claim it.
As a 23-year old full-time college student, you may be eligible to be claimed by your parents if you do not provide more than half your own support. If they are claiming you, they would also claim your education credit.
If you are not a dependent on your parents' return, then you may claim the credit for yourself. If you are unsure if your parents are including you on their tax return, you probably want to check with them before completing your own.
