Where do you keep getting that figure? The process is accurate up to 50-60,000 years.
Are you saying you accept the readings that show things to be 3500 years old or 3800 years old but all of a sudden if something is shown to be 4100 years old the science behind the process suddenly becomes inaccurate? That's not how the laws of physics work.
it;'s well known figures (though some folks argue for slightly longer period) even secular scientist sites will tell you this