Some people use that for dating the Earth as being 4.6 billions of years old...
(media.conspiracies.win)
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C14 does not enter atmosphere, it is created in it by ionizing radiation. Flux of radiation in the past could be estimated by other means (f.e. by other elements isotopes), and looks like it was relatively stable.
Rate of decay is very stable thing, it could not be changed by anything except exposure to ionising radiation that will make sample "younger" by creation of new C14 among captured carbon. It is concentration of C14 could be different at the time of capture in the plant.
You are partially right, you will get +- thousands of years for dates over tens thousands years ago. For thousands of years you will get +- century accuracy.
As you might know, history is not the science at all. It is an attempt of humanity to describe its deeds, not learning nature secrets. So it is not a surprise historians are not very honest in scientific sense, especially if they have specific narrative they need to follow.
Aluminium 26, for example.
What do you mean by "naturally occuring metal"? It's not about metal, it's about element. And aluminium is very common element on earth, in form of clay and many other minerals. All that minerals include aluminium that have isotope that decaying and created constantly by cosmic radiation if exposed to it. Half-life of aluminium-26 is 700 000 years.