What you "always thought" has been incorrect. A dependent does not get to choose whether they want to be claimed or not. The dependent does not have the power to choose or give permission to be claimed. The rule is if the dependent CAN be claimed they must say on their own tax return that they can be claimed as a dependent on someone else's tax return even if the person does not claim them.
You are not required to claim your dependent if for some reason you do not want to, but that does not release your dependent to say they cannot be claimed.
See below:
https://ttlc.intuit.com/community/dependents/help/when-do-i-have-to-answer-yes-to-being-claimed-as-a...
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**