Yes, they clearly have the right. When you opened the account with the CU, they probably did their initial credit pull under FCRA 604(a)(3)(F), not based specifically on the extension of credit, but rather in connection with a business transaction initiated by the consumer.
Now, you are requesting the additonal consideration of extension of credit. They have no way of knowing what other credit, derogs, etc., have occured since you opened your account. Unless it is for a very small amount of credit, or maybe a secured CC, they will most probably want to take a new look at your current credit report before putting money or credit on the table. You might call them in advance, and ask them to report any new inquiry as a soft inquiry, since little time has expired since their last credit pull. But that is up to them.