I tried a basic reproduction and was able to add CNAME record without any issues.
Please note that Google Groups is a place for non-technical how-to questions. Therefore, I would recommend you to reach out to Server Fault [1], or Stack Overflow [2] where Google also participates that can help you find answers, troubleshoot problems.
Please provide the steps to reproduce including error messages/logs etc. when you post your issue over there (please make sure not to share any private information).