Licensing is regulated by state medical boards, where in many cases it isnt residency per se that is required but a period of minimum post-graduate training, anywhere from 1 to 3 years depending on the state. Fellowship would be post grad training. If the doctor you are referring to got a license thru a state with a 1 year minimum, had a two year fellowship, had a general surgical residency prior and did a modified 3 year neuro fellowship, or a combination with a waiver for previous work, he/she could get a license in a one state and then apply for a license in a different state via reciprocity.
State Specific Requirements for Initial Medical Licensure