That is why it is a Geiger counter. Low count, low threat. High count, high threat. To my knowledge you can't fake a dangerous amount of radiation.

Sure, but if you're shipping radioactive materials into the country, you probably want to wrap it in lead, or anything that'll keep it from damaging you while in transit, which means lower counts, right?

Yes, lead can mask a highly radioactive object in transit. But I don't see what that has to do with false positives?

I figure that even a small amount of detected radiation would make people worry - "oh no, a terrorist is trying to smuggle plutonium into the country but his lead-lined briefcase has a hole in it!" - so generating a lot of false positives might cloak an actual delivery.

Or it could just cause panic, akin to calling in random bomb threats. Terrorism doesn't really have to kill anyone, just has to scare them.