I'm pretty sure that's what I said. That being said, in three states I have practiced, (only one with a training license, to be sure) a training license was only good within the supervision of the training institution.
This is the OP's problem. s/He can, under the terms of his license only practice under the supervision of his program. It is likely that his family/friends are not patients of that institution and not in clinic there. Ergo, if he prescribes outside of supervision, he is in violation of the training license. Not somewhere I would have gone, personally.
Once the resident does qualify and obtains a permanent and unrestricted medical license, and he want to write Rx for his friends and neighbors, including the "big gun" antibiotics, he is free to do so. The requirement for ID is institution dependent and will vary by institution, even within states.
All training institutions have a DEA number for its residents to use. The DEA requires a permanent and unrestricted license to issue the DEA number. It cannot be obtained by interns who cannot get a permanent unrestricted license. Many states now require two years of residency before issuing the licence.
I agree with Doc-B that CMS non-participators are rare, but residents are non-participating, by definition. CMS is bribing a training program to put up with them (at least that's what the institutions would have us believe). Interns cannot legally bill Medicare.
Records must be kept, but HIPAA gives wide latitude to the format, unless you are billing someone. The information must be protected, but if you have a yellow pad in a locked drawer that documents the visit, you have a medical record. And you must keep a record to document the need for the Rx.