To illustrate the extreme sensitivity of radioactivity measurements, let's take the example of the analysis carried out at the CENBG laboratory in Bordeaux of a bottle of Grand Cru which turned out to be a fake. Traces of cesium-137 were found in this bottle, a radioelement spread in the atmosphere during nuclear tests in the 1950s but which did not exist in 1928, the supposed vintage of this bottle sold as a Bordeaux Grand Cru Classé.
The presence of cesium-137 was demonstrated using an experimental device specializing in measurements of very low radioactivities. The bottle was placed in a lead shielded enclosure to reduce the gamma rays from natural radioactivity. Cesium-137 emits a gamma ray of 662 keV, with a very characteristic energy, which undoubtedly indicates its presence. During the 6 days that the measurement lasted, an excess of 330 counts in the vicinity of 662 keV was recorded, one count every 26 minutes! The measured activity was a few hundredths of a becquerel. The scam's signature cesium-137 amount was 0.2 millionth of a billionth of a gram!
No doubt this report caused many wine lovers to take their own bottles of Bordeaux Grand Cru Classé to the local nuclear reactor center to be stored with other radioactive waste.
What we have here is a failure of Quantitacy. We can detect radioactivity (as well as many other hazardous materials) at levels millions of times lower than anything we should ever worry about. Zero Tolerance is for fools. There is not zero of anything that we know exists.