Exactly.
You have to file federal paperwork for a license to the FCC. Social security number and all.
There must be some means in FedGov to flag a person and then have any filing in FedGov pop up and signal to someone who cares that this person of interest is doing such things.
Aside from that, traffic on the HAM bands is pretty low on average. Not tough to build an algorithm to pick it up, sample it, and then run it through a pattern matcher to detect encrypted comms. From there its a straight ‘fox hunt’, where you triangulate to find the transmission source.
I guess you can rig a system that would ‘spoof’ a radio signal. If you were to fox hunt that, it would be obvious that the signal you isolated was wired to a box or a computer that transmitted and received messages from some other physical location. Then it would be obvious something was very wrong.
You have to do more than that.
You have to pass a test administered by Volunteer Examiners at a scheduled exam session. The exam she probably took consists of thirty questions drawn from a pool of about 400 or so questions. Questions topics range from FCC regulations, operating protocols, allocated frequencies, and radio and electronic theory.
Nellie is no dummy, having earned a PHD and reading Russian fluently, so she could have researched how to get licensed and learned the material on her own. It would have been much easier with a licensed HAM to tutor her.
Nellie claims to have been "underemployed" during the time in question and to have attended a class in emergency response, wherein it was mentioned that a HAM radio license could allow one to communicate during a disaster when electricity and phone services are out. That is true.
Many HAM radio clubs conduct classes to prepare people to get qualified. Whoever asked her the questions about her HAM license should have probed a little deeper into what her process had been, where she took the exam, who, if anyone, helped her prepare, and who advised her on what equipment to purchase. It seems to me that none of the questioners were HAM radio licensees so that might explain why they were not prepared to delve deeper.