Yes, exactly. I knew this, which is why i was confused - but after reading your explanation it does make sense that C has the ability to increase the fee for both transactions without anything being invalidated.
But using replace-by-fee can be of low fee, instead of using child-pay-for-parent.
If you are buying items on online stores, you can use child-pay-for-parent because the transaction would be replaced with new txid. But I have used RBF to increase the fee while sending to centralized exchanges and while sending to friends without any complain. If not necessary to use CPFP, it is better you use a wallet that is supporting RBF and use it instead for low fee.