That argument relies on independent samples, but if someone's beaming radiation at the device to control its output, the samples will not be independent.
It's not that easy to control radiation, controlling it to the level of individual decays is not possible.
The closest you can get is bring it closer/further, or shield/unshield.
I'd rather use a local source in a Faraday cage, so that it's not possible for someone to influence the output at all.
A Faraday cage is not going to block this type of radiation.
To test, I made a simple script generating the dispersion graph: the numbers seem to be of good quality