AOTC- do I have to check 'someone can claim as dependent' if they dont?

The TT interview is clear that if a student can be claimed by parents as a dependent, *even if the parents don't claim the student on the parents return*, that the student must check the box that they can be claimed as a dependent. Also reference this:

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/indicate-claimed-dependent-so...

 

However I can't find anything on the IRS site that is this explicit.  The 1040 instructions for checking this box just say "if you can be claimed as a dependent on someone else's return".  I have a feeling students don't check it if their parents don't claim them.  "If you can be claimed" is pretty close to "have you been claimed".

If a parent doesn't meet the AGI requirements for claiming the AOTC then if the student claims it it can be a big savings for the student while the parent only loses $500.  However if the student checks the box that they can be claimed on the parent's return they cannot claim the AOTC.

What am I asking?  Not really sure but I don't want to miss saving money if it's not necessary.