Yes, that is correct. As both @Hal_Al and @xmasbaby0 said in order for your parents to claim the education credit, you must be listed on their tax return as a dependent. If they are unable to claim the credit, then you can claim the education credit.
Look at it this way, at least someone is getting the credit and it is not going to waste. Also, I have seen it where the dependent claims the credit and then gives the refund to their parents.
@dheil218
