Most states require prints to get your license.
The DEA requires you to give your prints to get a DEA license to dispense meds.
Unless I have forgotten, I have never given prints to anyone, and I have had a DEA number for 20+ years.
Quote from the DEA website:
Question – What does a practitioner/physician need to obtain before they can complete an application for DEA registration?
Answer – Issuance of a DEA registration to prescribe controlled substances is predicated on successfully completing all of the requirements imposed by the state in which the practitioner will conduct business and obtaining a state license. If the practitioner fails to obtain the required state license or has the license revoked or rescinded, then the DEA cannot issue the requested registration. If an existing DEA registrant looses their state privileges, then the DEA must also rescind or revoke their federal authority to prescribe controlled substances.
No mention of fingerprints.
I guess some states and hospitals might require it, but not in my experience.