Non-competes are not enforceable against non-exempt workers (i.e., hourly, part-time, or independent contractors) in most states, but especially in blue states.
In some states, including California, non-competes are not even enforceable against full-time, fairly high-level employees.
You or the intern needs to talk to a lawyer, b/c it sounds like the NLRB should be having a chat with the potential employee's former employer.
Forget about a lawyer, the intern should call the state's labor board.
They'll cut them down to size for free and be thrilled to do it.
Seriously, I often see advice on HN to lawyer up over an employee disagreement, but your home state's government probably already has a ton of people waiting to jump all over that situation for you. The laws are so employee-friendly it's often pretty unfair.
Even if the intern is justified in doing so, taking legal/regulatory action might not be the best way to start a career. A company this unreasonable may actually enjoy personal and professional destruction.
In some states, including California, non-competes are not even enforceable against full-time, fairly high-level employees.
You or the intern needs to talk to a lawyer, b/c it sounds like the NLRB should be having a chat with the potential employee's former employer.