The problem is differentiation from background.

A release from NK or Russia, by the time it hits your Geiger counter, will likely be so low that it will be lost in the noise of background radiation. And local sources (such as radon gas) would mask anything but significant nearby events.

The reason why France identified the release is because their detectors can determine different radioisotopes.

It's a little like the difference between a photovoltaic cell and a camera. Your Geiger counter can tell when the "light's on" (presence of radiation) but it takes a different instrument to determine that it's Ruthenium 106.

GGP spoke about general levels, not specific elements, and yes, you are 100% right, a Geiger counter is a pretty blunt instrument.

Even after Chernobyl and Fukushima, outside of the impacted area, there really wasn't any detectable increase in background.

You're much more likely to get an increase in background going into your basement (because of Radon daughters) than from an nuclear release halfway around the planet.

I did some research on this. James Mahaffey who is a nuclear engineer talks about this a bit in his book 'Atomic Adventures.': "Professional-grade Geiger counters, such as the Eberline E-120, are available as surplus, but they are usually sold without the probe assemble, which is what wears out when in constant use in a nuclear power facility. The probe is the expensive part, and installation of a new one will require calibration."