You've already been given one reason why this isn't good science (it is arguable that it is science).
They have not taken into account all known processes. C14 can be formed in situ if the material is near radioactive ores. Interestingly this can create amounts enough to bring measured age within the most extreme limits of carbon dating.
Unless this is accounted for the results can not be taken as you source suggests.
Fortunately people who actually know how to use carbon dating aren't so foolish as those of your source. They do not attempt to use it when it is out of it's range of applicability. Doing so it, at best, bad science, and, at worst not science at all but rather is dishonesty.