No, yes, and no.
A medical student does not have an MD degree, and therefore no license. They cannot bill. A first year RESIDENT (and that may be why they identified themselves as a student) can see and treat patients, but not independent of oversight by an attending (typically has to review each case directly, as well as any diagnostic adjuncts. Many don't necessarily see the patient themselves.). They also have no license until they have completed their first year of residency, Step 3 of the USMLE, and complete the state's licensing process.
Billing for this without being seen by a physician is fraud. Without a physical examination, you can't bill at that level either unless you are a psychologist. A level 5 coding requires examination of a certain number of body systems, history points to include medical, family, and social history, and a review of several body systems (ROS). Call the billing company and explain this, and they should write it off. If they push back, mention the fact that an actual doctor found it was due to a dangerous condition, and that should also make them lean toward writing it off.
What probably happened is that the doc probably got busy, staffed the patient with the student, then didn't see you though the medical student thought he did.
'zilla