Nurses do not have a license to practice medicine. They are functioning as an extender of care for the physician under the doctors supervision. In different states, supervision can be done by phone and not necessarily in person. However, as a patient, you should be able to ask to have the doctor check on you. So there must be some provision to have the doctor see you at some point for any problem. In addition, in some states, the doctor must see you before treatment in order to perform a good faith exam. Ultimately it is the doctor's license which is being used to treat you but both must have licenses for that state.
Every state has different rules regarding a physician's supervision of a nurse or PA injector. Supervision may need to be direct (on site) or indirect (off site but available by phone or communication). You may also need a supervision agreement between you and the physician provider. You should check with your state nursing board, your liability insurance provider or a health care attorney for a definitive opinion on the rules in your state.