It has been well known carbon dating is not the most accurate for decades. They do not use this method to determine the age of the earth. As far as archaeology, how do you think they figured our carbon dating is flawed. There are many methods to date things. The older we go the larger the range of dates possible. When you are dealing with a timescale of 6.4 GA what is an error of +-50 years? We know with certainty that humans have been around 200K years. So what if we get the date of the shroud of turin wrong.