Now that's interesting - I hadn't heard of cancer radiation treatments being performed with proton and fast-neutron beams, which can indeed cause activation of the subject material. I was mostly guessing at cancer treatments, given the weird reference in the GP post to Chemotherapy. Certainly there are other treatments that do result in increased radioactivity of the patient after treatment.

Nevertheless, I would still find it pretty surprising if any of these sources could be reliably detected from inside a moving vehicle by a stationary sensor. Or that cases of these medical treatments would not be overwhelmed by other incidental sources of radiation being slightly higher or lower than usual.

Regarding background sources, the fact that the target of interest is moving could actually be a great benefit for background rejection. Place two detectors on the path separated by some distance, knowing how long it takes for a typical vehicle to travel between them, and you can filter out simultaneous spikes as background fluctuation. Modern photon counting detectors are pretty amazing, and it would take only a small number of temporally correlated discrete events at each detector to reach the probability threshold of alarm.

I don't work on these systems, obviously - those who do aren't talking - and this is just idle speculation. But I do know that lots of DHS money is shoveled into R&D on this kind of thing every year and I would not be surprised if some of the tech does work.